LMFDB - Embedded newform 245.2.x.a.108.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,2,Mod(3,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([63, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.x (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$624$
Relative dimension:	$26$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			108.23
Character	$\chi$	$=$	245.108
Dual form			245.2.x.a.152.23

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.70168 - 1.25589i) q^{2} +(0.365908 - 1.93387i) q^{3} +(0.728921 - 2.36310i) q^{4} +(-1.92148 - 1.14364i) q^{5} +(-1.80608 - 3.75036i) q^{6} +(1.11418 + 2.39971i) q^{7} +(-0.330380 - 0.944171i) q^{8} +(-0.813339 - 0.319212i) q^{9} +(-4.70603 + 0.467072i) q^{10} +(0.0928530 + 0.236585i) q^{11} +(-4.30321 - 2.27432i) q^{12} +(-0.251221 - 2.22965i) q^{13} +(4.90975 + 2.68423i) q^{14} +(-2.91473 + 3.29743i) q^{15} +(2.33855 + 1.59440i) q^{16} +(0.143238 + 3.82813i) q^{17} +(-1.78494 + 0.478272i) q^{18} +(-1.87492 - 3.24746i) q^{19} +(-4.10315 + 3.70704i) q^{20} +(5.04841 - 1.27661i) q^{21} +(0.455132 + 0.285978i) q^{22} +(-4.52997 - 0.169500i) q^{23} +(-1.94679 + 0.293432i) q^{24} +(2.38418 + 4.39496i) q^{25} +(-3.22770 - 3.47863i) q^{26} +(2.22649 - 3.54343i) q^{27} +(6.48291 - 0.883728i) q^{28} +(0.249778 + 0.0570102i) q^{29} +(-0.818715 + 9.27175i) q^{30} +(6.33821 + 3.65937i) q^{31} +(7.98106 - 0.298630i) q^{32} +(0.491501 - 0.0929970i) q^{33} +(5.05147 + 6.33434i) q^{34} +(0.603523 - 5.88522i) q^{35} +(-1.34719 + 1.68932i) q^{36} +(0.293479 - 0.555290i) q^{37} +(-7.26897 - 3.17142i) q^{38} +(-4.40377 - 0.330017i) q^{39} +(-0.444973 + 2.19204i) q^{40} +(-3.39316 + 7.04597i) q^{41} +(6.98747 - 8.51264i) q^{42} +(0.237634 + 0.0831519i) q^{43} +(0.626758 - 0.0469691i) q^{44} +(1.19775 + 1.54353i) q^{45} +(-7.92142 + 5.40073i) q^{46} +(-5.86776 - 7.95053i) q^{47} +(3.93905 - 3.93905i) q^{48} +(-4.51720 + 5.34742i) q^{49} +(9.57670 + 4.48453i) q^{50} +(7.45551 + 1.12374i) q^{51} +(-5.45201 - 1.03158i) q^{52} +(-5.10608 - 9.66117i) q^{53} +(-0.661417 - 8.82600i) q^{54} +(0.0921533 - 0.560785i) q^{55} +(1.89763 - 1.84479i) q^{56} +(-6.96621 + 2.43758i) q^{57} +(0.496640 - 0.216682i) q^{58} +(-0.928629 + 12.3917i) q^{59} +(5.66755 + 9.29138i) q^{60} +(-2.88820 - 9.36330i) q^{61} +(15.3814 - 1.73306i) q^{62} +(-0.140191 - 2.30744i) q^{63} +(8.78041 - 7.00214i) q^{64} +(-2.06720 + 4.57154i) q^{65} +(0.719581 - 0.775524i) q^{66} +(2.95256 + 11.0191i) q^{67} +(9.15067 + 2.45192i) q^{68} +(-1.98534 + 8.69835i) q^{69} +(-6.36421 - 10.7727i) q^{70} +(2.31287 + 10.1333i) q^{71} +(-0.0326800 + 0.873392i) q^{72} +(-0.0908966 + 0.123161i) q^{73} +(-0.197979 - 1.31350i) q^{74} +(9.37167 - 3.00253i) q^{75} +(-9.04075 + 2.06349i) q^{76} +(-0.464281 + 0.486419i) q^{77} +(-7.90826 + 4.96909i) q^{78} +(0.348481 - 0.201196i) q^{79} +(-2.67006 - 5.73806i) q^{80} +(-7.95933 - 7.38518i) q^{81} +(3.07493 + 16.2514i) q^{82} +(-16.3546 - 1.84272i) q^{83} +(0.663132 - 12.8605i) q^{84} +(4.10277 - 7.51949i) q^{85} +(0.508807 - 0.156946i) q^{86} +(0.201646 - 0.462178i) q^{87} +(0.192700 - 0.165832i) q^{88} +(0.234099 - 0.596475i) q^{89} +(3.97669 + 1.12233i) q^{90} +(5.07060 - 3.08709i) q^{91} +(-3.70254 + 10.5812i) q^{92} +(9.39594 - 10.9183i) q^{93} +(-19.9700 - 6.15994i) q^{94} +(-0.111297 + 8.38416i) q^{95} +(2.34282 - 15.5436i) q^{96} +(0.348307 + 0.348307i) q^{97} +(-0.971017 + 14.7727i) q^{98} -0.222064i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} - 34 q^{10} - 56 q^{11} - 34 q^{12} - 28 q^{13} + 12 q^{15} - 100 q^{16} - 26 q^{17} - 10 q^{18} - 28 q^{20} - 76 q^{21} - 48 q^{22}+ \cdots + 304 q^{98}+O(q^{100}) $ 624 * q - 26 * q^2 - 22 * q^3 - 28 * q^5 - 28 * q^6 - 18 * q^7 - 24 * q^8 - 34 * q^10 - 56 * q^11 - 34 * q^12 - 28 * q^13 + 12 * q^15 - 100 * q^16 - 26 * q^17 - 10 * q^18 - 28 * q^20 - 76 * q^21 - 48 * q^22 - 34 * q^23 - 24 * q^25 - 60 * q^26 - 28 * q^27 - 46 * q^28 - 10 * q^30 - 60 * q^31 + 54 * q^32 - 28 * q^33 - 20 * q^35 + 116 * q^36 - 20 * q^37 + 12 * q^38 - 46 * q^40 - 114 * q^42 - 24 * q^43 + 60 * q^45 + 108 * q^46 - 94 * q^47 - 296 * q^50 + 52 * q^51 - 52 * q^52 - 106 * q^53 + 14 * q^55 + 96 * q^56 + 72 * q^57 - 142 * q^58 - 26 * q^60 + 80 * q^61 - 56 * q^62 - 24 * q^63 - 20 * q^65 - 240 * q^66 - 8 * q^67 - 30 * q^68 + 180 * q^70 + 48 * q^71 + 138 * q^72 - 4 * q^73 - 106 * q^75 + 56 * q^76 - 8 * q^77 - 204 * q^78 - 18 * q^80 - 284 * q^81 - 162 * q^82 + 182 * q^83 - 36 * q^85 - 76 * q^86 - 74 * q^87 + 288 * q^88 - 112 * q^90 + 44 * q^91 - 8 * q^92 + 368 * q^93 + 26 * q^95 + 136 * q^96 + 304 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.70168	−	1.25589i	1.20327	−	0.888051i	0.207344	−	0.978268i	$-0.433518\pi$
$2$	1.70168	−	1.25589i	1.20327	−	0.888051i	0.995922	+	0.0902168i	$0.0287560\pi$
$3$	0.365908	−	1.93387i	0.211257	−	1.11652i	−0.702940	−	0.711249i	$-0.748130\pi$
$3$	0.365908	−	1.93387i	0.211257	−	1.11652i	0.914197	−	0.405270i	$-0.132823\pi$
$4$	0.728921	−	2.36310i	0.364460	−	1.18155i
$5$	−1.92148	−	1.14364i	−0.859312	−	0.511451i
$5$	−1.92148	−	1.14364i	−0.859312	−	0.511451i
$6$	−1.80608	−	3.75036i	−0.737328	−	1.53108i
$7$	1.11418	+	2.39971i	0.421121	+	0.907004i
$7$	1.11418	+	2.39971i	0.421121	+	0.907004i
$8$	−0.330380	−	0.944171i	−0.116807	−	0.333815i
$9$	−0.813339	−	0.319212i	−0.271113	−	0.106404i
$10$	−4.70603	+	0.467072i	−1.48818	+	0.147701i
$11$	0.0928530	+	0.236585i	0.0279962	+	0.0713332i	0.944188	−	0.329406i	$-0.106849\pi$
$11$	0.0928530	+	0.236585i	0.0279962	+	0.0713332i	−0.916192	+	0.400739i	$0.868753\pi$
$12$	−4.30321	−	2.27432i	−1.24223	−	0.656538i
$13$	−0.251221	−	2.22965i	−0.0696762	−	0.618394i	−0.979222	−	0.202790i	$-0.934999\pi$
$13$	−0.251221	−	2.22965i	−0.0696762	−	0.618394i	0.909546	−	0.415603i	$-0.136430\pi$
$14$	4.90975	+	2.68423i	1.31219	+	0.717391i
$15$	−2.91473	+	3.29743i	−0.752581	+	0.851392i
$16$	2.33855	+	1.59440i	0.584638	+	0.398599i
$17$	0.143238	+	3.82813i	0.0347404	+	0.928457i	0.902296	+	0.431117i	$0.141880\pi$
$17$	0.143238	+	3.82813i	0.0347404	+	0.928457i	−0.867556	+	0.497340i	$0.834310\pi$
$18$	−1.78494	+	0.478272i	−0.420713	+	0.112730i
$19$	−1.87492	−	3.24746i	−0.430136	−	0.745018i	0.566748	−	0.823891i	$-0.308201\pi$
$19$	−1.87492	−	3.24746i	−0.430136	−	0.745018i	−0.996885	+	0.0788729i	$0.974868\pi$
$20$	−4.10315	+	3.70704i	−0.917491	+	0.828918i
$21$	5.04841	−	1.27661i	1.10165	−	0.278579i
$22$	0.455132	+	0.285978i	0.0970344	+	0.0609708i
$23$	−4.52997	−	0.169500i	−0.944565	−	0.0353431i	−0.439331	−	0.898326i	$-0.644784\pi$
$23$	−4.52997	−	0.169500i	−0.944565	−	0.0353431i	−0.505234	+	0.862982i	$0.668594\pi$
$24$	−1.94679	+	0.293432i	−0.397387	+	0.0598965i
$25$	2.38418	+	4.39496i	0.476835	+	0.878993i
$26$	−3.22770	−	3.47863i	−0.633004	−	0.682216i
$27$	2.22649	−	3.54343i	0.428487	−	0.681934i
$28$	6.48291	−	0.883728i	1.22515	−	0.167009i
$29$	0.249778	+	0.0570102i	0.0463826	+	0.0105865i	0.245649	−	0.969359i	$-0.420999\pi$
$29$	0.249778	+	0.0570102i	0.0463826	+	0.0105865i	−0.199267	+	0.979945i	$0.563856\pi$
$30$	−0.818715	+	9.27175i	−0.149476	+	1.69278i
$31$	6.33821	+	3.65937i	1.13838	+	0.657242i	0.946028	−	0.324085i	$-0.105056\pi$
$31$	6.33821	+	3.65937i	1.13838	+	0.657242i	0.192348	+	0.981327i	$0.438390\pi$
$32$	7.98106	−	0.298630i	1.41087	−	0.0527909i
$33$	0.491501	−	0.0929970i	0.0855593	−	0.0161887i
$34$	5.05147	+	6.33434i	0.866320	+	1.08633i
$35$	0.603523	−	5.88522i	0.102014	−	0.994783i
$36$	−1.34719	+	1.68932i	−0.224532	+	0.281554i
$37$	0.293479	−	0.555290i	0.0482477	−	0.0912891i	−0.858813	−	0.512290i	$-0.828797\pi$
$37$	0.293479	−	0.555290i	0.0482477	−	0.0912891i	0.907060	+	0.421001i	$0.138321\pi$
$38$	−7.26897	−	3.17142i	−1.17918	−	0.514472i
$39$	−4.40377	−	0.330017i	−0.705168	−	0.0528451i
$40$	−0.444973	+	2.19204i	−0.0703564	+	0.346592i
$41$	−3.39316	+	7.04597i	−0.529923	+	1.10040i	0.448500	+	0.893783i	$0.351958\pi$
$41$	−3.39316	+	7.04597i	−0.529923	+	1.10040i	−0.978423	+	0.206613i	$0.933756\pi$
$42$	6.98747	−	8.51264i	1.07819	−	1.31353i
$43$	0.237634	+	0.0831519i	0.0362389	+	0.0126805i	0.348338	−	0.937369i	$-0.386746\pi$
$43$	0.237634	+	0.0831519i	0.0362389	+	0.0126805i	−0.312099	+	0.950050i	$0.601032\pi$
$44$	0.626758	−	0.0469691i	0.0944874	−	0.00708085i
$45$	1.19775	+	1.54353i	0.178550	+	0.230095i
$46$	−7.92142	+	5.40073i	−1.16795	+	0.796294i
$47$	−5.86776	−	7.95053i	−0.855900	−	1.15970i	−0.985758	−	0.168171i	$-0.946214\pi$
$47$	−5.86776	−	7.95053i	−0.855900	−	1.15970i	0.129857	−	0.991533i	$-0.458548\pi$
$48$	3.93905	−	3.93905i	0.568553	−	0.568553i
$49$	−4.51720	+	5.34742i	−0.645314	+	0.763917i
$50$	9.57670	+	4.48453i	1.35435	+	0.634208i
$51$	7.45551	+	1.12374i	1.04398	+	0.157355i
$52$	−5.45201	−	1.03158i	−0.756058	−	0.143054i
$53$	−5.10608	−	9.66117i	−0.701374	−	1.32706i	−0.934969	−	0.354730i	$-0.884573\pi$
$53$	−5.10608	−	9.66117i	−0.701374	−	1.32706i	0.233595	−	0.972334i	$-0.424951\pi$
$54$	−0.661417	−	8.82600i	−0.0900075	−	1.20107i
$55$	0.0921533	−	0.560785i	0.0124260	−	0.0756162i
$56$	1.89763	−	1.84479i	0.253582	−	0.246521i
$57$	−6.96621	+	2.43758i	−0.922697	+	0.322866i
$58$	0.496640	−	0.216682i	0.0652120	−	0.0284517i
$59$	−0.928629	+	12.3917i	−0.120897	+	1.61326i	0.525864	+	0.850569i	$0.323742\pi$
$59$	−0.928629	+	12.3917i	−0.120897	+	1.61326i	−0.646761	+	0.762693i	$0.723877\pi$
$60$	5.66755	+	9.29138i	0.731677	+	1.19951i
$61$	−2.88820	−	9.36330i	−0.369796	−	1.19885i	−0.929082	−	0.369873i	$-0.879401\pi$
$61$	−2.88820	−	9.36330i	−0.369796	−	1.19885i	0.559287	−	0.828974i	$-0.311075\pi$
$62$	15.3814	−	1.73306i	1.95343	−	0.220099i
$63$	−0.140191	−	2.30744i	−0.0176625	−	0.290710i
$64$	8.78041	−	7.00214i	1.09755	−	0.875267i
$65$	−2.06720	+	4.57154i	−0.256404	+	0.567029i
$66$	0.719581	−	0.775524i	0.0885743	−	0.0954604i
$67$	2.95256	+	11.0191i	0.360713	+	1.34620i	0.873141	+	0.487468i	$0.162079\pi$
$67$	2.95256	+	11.0191i	0.360713	+	1.34620i	−0.512428	+	0.858730i	$0.671254\pi$
$68$	9.15067	+	2.45192i	1.10968	+	0.297338i
$69$	−1.98534	+	8.69835i	−0.239007	+	1.04716i
$70$	−6.36421	−	10.7727i	−0.760668	−	1.28758i
$71$	2.31287	+	10.1333i	0.274487	+	1.20261i	0.904654	+	0.426146i	$0.140129\pi$
$71$	2.31287	+	10.1333i	0.274487	+	1.20261i	−0.630168	+	0.776459i	$0.717014\pi$
$72$	−0.0326800	+	0.873392i	−0.00385138	+	0.102930i
$73$	−0.0908966	+	0.123161i	−0.0106386	+	0.0144148i	−0.809885	−	0.586589i	$-0.800470\pi$
$73$	−0.0908966	+	0.123161i	−0.0106386	+	0.0144148i	0.799246	+	0.601004i	$0.205232\pi$
$74$	−0.197979	−	1.31350i	−0.0230145	−	0.152691i
$75$	9.37167	−	3.00253i	1.08215	−	0.346703i
$76$	−9.04075	+	2.06349i	−1.03705	+	0.236699i
$77$	−0.464281	+	0.486419i	−0.0529097	+	0.0554326i
$78$	−7.90826	+	4.96909i	−0.895435	+	0.562639i
$79$	0.348481	−	0.201196i	0.0392072	−	0.0226363i	−0.480268	−	0.877122i	$-0.659461\pi$
$79$	0.348481	−	0.201196i	0.0392072	−	0.0226363i	0.519475	+	0.854485i	$0.326127\pi$
$80$	−2.67006	−	5.73806i	−0.298522	−	0.641535i
$81$	−7.95933	−	7.38518i	−0.884370	−	0.820575i
$82$	3.07493	+	16.2514i	0.339569	+	1.79467i
$83$	−16.3546	−	1.84272i	−1.79515	−	0.202264i	−0.849529	−	0.527543i	$-0.823113\pi$
$83$	−16.3546	−	1.84272i	−1.79515	−	0.202264i	−0.945618	+	0.325278i	$0.894542\pi$
$84$	0.663132	−	12.8605i	0.0723536	−	1.40319i
$85$	4.10277	−	7.51949i	0.445008	−	0.815603i
$86$	0.508807	−	0.156946i	0.0548660	−	0.0169239i
$87$	0.201646	−	0.462178i	0.0216187	−	0.0495506i
$88$	0.192700	−	0.165832i	0.0205419	−	0.0176778i
$89$	0.234099	−	0.596475i	0.0248145	−	0.0632262i	−0.917930	−	0.396743i	$-0.870140\pi$
$89$	0.234099	−	0.596475i	0.0248145	−	0.0632262i	0.942744	+	0.333517i	$0.108236\pi$
$90$	3.97669	+	1.12233i	0.419180	+	0.118304i
$91$	5.07060	−	3.08709i	0.531544	−	0.323615i
$92$	−3.70254	+	10.5812i	−0.386016	+	1.10317i
$93$	9.39594	−	10.9183i	0.974313	−	1.13217i
$94$	−19.9700	−	6.15994i	−2.05975	−	0.635350i
$95$	−0.111297	+	8.38416i	−0.0114189	+	0.860197i
$96$	2.34282	−	15.5436i	0.239113	−	1.58641i
$97$	0.348307	+	0.348307i	0.0353652	+	0.0353652i	0.724568	−	0.689203i	$-0.242039\pi$
$97$	0.348307	+	0.348307i	0.0353652	+	0.0353652i	−0.689203	+	0.724568i	$0.742039\pi$
$98$	−0.971017	+	14.7727i	−0.0980875	+	1.49227i
$99$		−	0.222064i		−	0.0223183i
$100$	12.1236	−	2.43048i	1.21236	−	0.243048i
$101$	−0.571120	−	0.837680i	−0.0568286	−	0.0833522i	0.796773	−	0.604279i	$-0.206539\pi$
$101$	−0.571120	−	0.837680i	−0.0568286	−	0.0833522i	−0.853601	+	0.520927i	$0.825586\pi$
$102$	14.0982	−	7.45109i	1.39593	−	0.737768i
$103$	7.72958	+	6.65184i	0.761618	+	0.655426i	0.944798	−	0.327654i	$-0.106258\pi$
$103$	7.72958	+	6.65184i	0.761618	+	0.655426i	−0.183179	+	0.983080i	$0.558639\pi$
$104$	−2.02217	+	0.973827i	−0.198290	+	0.0954916i
$105$	−11.1604	−	3.32058i	−1.08914	−	0.324055i
$106$	−20.8223	−	10.0275i	−2.02244	−	0.973956i
$107$	2.36840	+	5.42844i	0.228962	+	0.524787i	0.992682	−	0.120761i	$-0.0385336\pi$
$107$	2.36840	+	5.42844i	0.228962	+	0.524787i	−0.763719	+	0.645549i	$0.776629\pi$
$108$	−6.75056	−	7.84430i	−0.649573	−	0.754818i
$109$	−9.15062	+	3.59135i	−0.876471	+	0.343989i	−0.760558	−	0.649270i	$-0.775075\pi$
$109$	−9.15062	+	3.59135i	−0.876471	+	0.343989i	−0.115913	+	0.993259i	$0.536979\pi$
$110$	−0.547471	−	1.07001i	−0.0521993	−	0.102021i
$111$	−0.966471	−	0.770735i	−0.0917334	−	0.0731549i
$112$	−1.22052	+	7.38829i	−0.115328	+	0.698127i
$113$	0.538131	−	4.77605i	0.0506231	−	0.449293i	−0.942675	−	0.333712i	$-0.891699\pi$
$113$	0.538131	−	4.77605i	0.0506231	−	0.449293i	0.993298	−	0.115580i	$-0.0368728\pi$
$114$	−8.79288	+	12.8968i	−0.823529	+	1.20790i
$115$	8.51041	+	5.50635i	0.793600	+	0.513469i
$116$	0.316789	−	0.548695i	0.0294132	−	0.0509451i
$117$	−0.507403	+	1.89365i	−0.0469094	+	0.175068i
$118$	13.9824	+	22.2529i	1.28719	+	2.04855i
$119$	−9.02680	+	4.60896i	−0.827485	+	0.422503i
$120$	4.07630	+	1.66260i	0.372114	+	0.151774i
$121$	8.01622	−	7.43796i	0.728747	−	0.676179i
$122$	−16.6741	−	12.3060i	−1.50960	−	1.11414i
$123$	12.3844	+	9.14010i	1.11666	+	0.824135i
$124$	13.2675	−	12.3105i	1.19146	−	1.10551i
$125$	0.445103	−	11.1715i	0.0398112	−	0.999207i
$126$	−3.13646	−	3.75044i	−0.279418	−	0.334116i
$127$	−10.8265	−	17.2303i	−0.960700	−	1.52895i	−0.844387	−	0.535733i	$-0.820035\pi$
$127$	−10.8265	−	17.2303i	−0.960700	−	1.52895i	−0.116313	−	0.993213i	$-0.537108\pi$
$128$	2.01327	−	7.51362i	0.177949	−	0.664116i
$129$	0.247757	−	0.429128i	0.0218138	−	0.0377826i
$130$	2.22366	+	10.3755i	0.195028	+	0.909988i
$131$	−4.56780	+	6.69973i	−0.399090	+	0.585358i	−0.972209	−	0.234114i	$-0.924781\pi$
$131$	−4.56780	+	6.69973i	−0.399090	+	0.585358i	0.573119	+	0.819472i	$0.305733\pi$
$132$	0.138504	−	1.22926i	0.0120552	−	0.106993i
$133$	5.70395	−	8.11752i	0.494595	−	0.703878i
$134$	18.8631	+	15.0428i	1.62953	+	1.29950i
$135$	−8.33056	+	4.26234i	−0.716980	+	0.366844i
$136$	3.56708	−	1.39998i	0.305875	−	0.120047i
$137$	−11.7047	−	13.6011i	−0.999997	−	1.16202i	−0.986774	−	0.162105i	$-0.948172\pi$
$137$	−11.7047	−	13.6011i	−0.999997	−	1.16202i	−0.0132231	−	0.999913i	$-0.504209\pi$
$138$	7.54580	+	17.2952i	0.642341	+	1.47226i
$139$	3.08412	+	1.48523i	0.261591	+	0.125976i	0.560083	−	0.828436i	$-0.310769\pi$
$139$	3.08412	+	1.48523i	0.261591	+	0.125976i	−0.298492	+	0.954412i	$0.596483\pi$
$140$	−13.4675	−	5.71604i	−1.13821	−	0.483094i
$141$	−17.5223	+	8.43831i	−1.47565	+	0.710634i
$142$	16.6621	+	14.3389i	1.39826	+	1.20330i
$143$	0.504176	−	0.266465i	0.0421613	−	0.0222829i
$144$	−1.39308	−	2.04328i	−0.116090	−	0.170273i
$145$	−0.414745	−	0.395200i	−0.0344427	−	0.0328196i
$146$			0.323736i			0.0267926i
$147$	8.68833	+	10.6923i	0.716602	+	0.881889i
$148$	−1.09828	−	1.09828i	−0.0902784	−	0.0902784i
$149$	3.39917	−	22.5520i	0.278470	−	1.84753i	−0.213531	−	0.976936i	$-0.568496\pi$
$149$	3.39917	−	22.5520i	0.278470	−	1.84753i	0.492001	−	0.870594i	$-0.336266\pi$
$150$	12.1767	−	16.8792i	0.994222	−	1.37818i
$151$	8.61664	+	2.65788i	0.701212	+	0.216295i	0.624804	−	0.780781i	$-0.285179\pi$
$151$	8.61664	+	2.65788i	0.701212	+	0.216295i	0.0764079	+	0.997077i	$0.475655\pi$
$152$	−2.44672	+	2.84314i	−0.198455	+	0.230609i
$153$	1.10548	−	3.15929i	0.0893730	−	0.255413i
$154$	−0.179165	+	1.41082i	−0.0144375	+	0.113687i
$155$	−7.99375	−	14.2800i	−0.642074	−	1.14700i
$156$	−3.98987	+	10.1660i	−0.319445	+	0.813933i
$157$	4.97655	−	4.28267i	0.397172	−	0.341794i	−0.430916	−	0.902392i	$-0.641810\pi$
$157$	4.97655	−	4.28267i	0.397172	−	0.341794i	0.828088	+	0.560598i	$0.189429\pi$
$158$	0.340321	−	0.780025i	0.0270745	−	0.0620554i
$159$	−20.5518	+	6.33939i	−1.62986	+	0.502746i
$160$	−15.6770	−	8.55364i	−1.23937	−	0.676225i
$161$	−4.64046	−	11.0595i	−0.365720	−	0.871608i
$162$	−22.8192	−	2.57111i	−1.79285	−	0.202005i
$163$	−2.22048	−	11.7355i	−0.173921	−	0.919197i	−0.955411	−	0.295279i	$-0.904587\pi$
$163$	−2.22048	−	11.7355i	−0.173921	−	0.919197i	0.781490	−	0.623918i	$-0.214460\pi$
$164$	14.1770	+	13.1543i	1.10704	+	1.02718i
$165$	−1.05076	−	0.383408i	−0.0818019	−	0.0298483i
$166$	−30.1444	+	17.4039i	−2.33966	+	1.35080i
$167$	21.1454	−	13.2865i	1.63628	−	1.02814i	0.681063	−	0.732225i	$-0.261518\pi$
$167$	21.1454	−	13.2865i	1.63628	−	1.02814i	0.955214	−	0.295916i	$-0.0956249\pi$
$168$	−2.87323	−	4.34480i	−0.221674	−	0.335208i
$169$	7.76584	−	1.77250i	0.597372	−	0.136346i
$170$	−2.46210	−	17.9484i	−0.188834	−	1.37658i
$171$	0.488319	+	3.23978i	0.0373427	+	0.247752i
$172$	0.369713	−	0.500944i	0.0281904	−	0.0381966i
$173$	−0.503672	+	13.4609i	−0.0382935	+	1.02342i	0.839199	+	0.543825i	$0.183024\pi$
$173$	−0.503672	+	13.4609i	−0.0382935	+	1.02342i	−0.877492	+	0.479591i	$0.840785\pi$
$174$	−0.237310	−	1.03972i	−0.0179904	−	0.0788211i
$175$	−7.89022	+	10.6181i	−0.596445	+	0.802654i
$176$	−0.160070	+	0.701312i	−0.0120657	+	0.0528633i
$177$	23.6241	+	6.33007i	1.77570	+	0.475797i
$178$	−0.350748	−	1.30901i	−0.0262897	−	0.0981145i
$179$	5.17088	−	5.57288i	0.386490	−	0.416537i	−0.509599	−	0.860412i	$-0.670206\pi$
$179$	5.17088	−	5.57288i	0.386490	−	0.416537i	0.896089	+	0.443875i	$0.146397\pi$
$180$	4.52058	−	1.70530i	0.336944	−	0.127106i
$181$	−17.5627	+	14.0058i	−1.30542	+	1.04104i	−0.309493	+	0.950902i	$0.600159\pi$
$181$	−17.5627	+	14.0058i	−1.30542	+	1.04104i	−0.995929	+	0.0901374i	$0.971269\pi$
$182$	4.75146	−	11.6214i	0.352202	−	0.861433i
$183$	−19.1642	+	2.15929i	−1.41666	+	0.159619i
$184$	1.33657	+	4.33307i	0.0985336	+	0.319438i
$185$	−1.19897	+	0.731344i	−0.0881497	+	0.0537695i
$186$	2.27664	−	30.3797i	0.166931	−	2.22755i
$187$	−0.892379	+	0.389341i	−0.0652572	+	0.0284714i
$188$	−23.0651	+	8.07081i	−1.68219	+	0.588624i
$189$	10.9839	+	1.39489i	0.798962	+	0.101463i
$190$	10.3402	+	14.4069i	0.750159	+	1.04519i
$191$	−1.23028	−	16.4170i	−0.0890202	−	1.18789i	−0.845537	−	0.533917i	$-0.820719\pi$
$191$	−1.23028	−	16.4170i	−0.0890202	−	1.18789i	0.756516	−	0.653975i	$-0.226900\pi$
$192$	−10.3284	−	19.5423i	−0.745388	−	1.41034i
$193$	8.74417	+	1.65449i	0.629419	+	0.119092i	0.490827	−	0.871257i	$-0.336695\pi$
$193$	8.74417	+	1.65449i	0.629419	+	0.119092i	0.138592	+	0.990350i	$0.455742\pi$
$194$	1.03014	+	0.155269i	0.0739599	+	0.0111477i
$195$	8.08435	+	5.67045i	0.578932	+	0.406070i
$196$	9.34383	+	14.5725i	0.667416	+	1.04089i
$197$	6.97032	−	6.97032i	0.496615	−	0.496615i	−0.413768	−	0.910383i	$-0.635787\pi$
$197$	6.97032	−	6.97032i	0.496615	−	0.496615i	0.910383	+	0.413768i	$0.135787\pi$
$198$	−0.278889	−	0.377881i	−0.0198198	−	0.0268548i
$199$	3.32613	−	2.26772i	0.235783	−	0.160754i	−0.439665	−	0.898162i	$-0.644903\pi$
$199$	3.32613	−	2.26772i	0.235783	−	0.160754i	0.675448	+	0.737408i	$0.263950\pi$
$200$	3.36191	−	3.70308i	0.237723	−	0.261847i
$201$	22.3899	−	1.67789i	1.57926	−	0.118349i
$202$	−2.02390	−	0.708193i	−0.142401	−	0.0498283i
$203$	0.141490	+	0.662914i	0.00993066	+	0.0465275i
$204$	8.08999	−	16.7990i	0.566412	−	1.17617i
$205$	14.5779	−	9.65814i	1.01817	−	0.674554i
$206$	21.5073	+	1.61175i	1.49848	+	0.112296i
$207$	3.63030	+	1.58388i	0.252323	+	0.110087i
$208$	2.96745	−	5.61470i	0.205756	−	0.389309i
$209$	0.594210	−	0.745115i	0.0411023	−	0.0515407i
$210$	−23.1617	+	8.36573i	−1.59831	+	0.577290i
$211$	6.86801	+	8.61221i	0.472813	+	0.592889i	0.959857	−	0.280488i	$-0.0904963\pi$
$211$	6.86801	+	8.61221i	0.472813	+	0.592889i	−0.487044	+	0.873377i	$0.661925\pi$
$212$	−26.5523	+	5.02396i	−1.82362	+	0.345047i
$213$	20.4428	−	0.764917i	1.40072	−	0.0524112i
$214$	10.8478	+	6.26298i	0.741541	+	0.428129i
$215$	−0.361514	−	0.431543i	−0.0246551	−	0.0294310i
$216$	−4.08119	−	0.931505i	−0.277690	−	0.0633809i
$217$	−1.71950	+	19.2871i	−0.116727	+	1.30929i
$218$	−11.0610	+	17.6035i	−0.749148	+	1.19226i
$219$	0.204917	+	0.220847i	0.0138470	+	0.0149235i
$220$	−1.25802	−	0.626536i	−0.0848157	−	0.0422410i
$221$	8.49940	−	1.28108i	0.571732	−	0.0861747i
$222$	−2.61258	−	0.0977559i	−0.175345	−	0.00656095i
$223$	−1.58284	−	0.994562i	−0.105995	−	0.0666008i	0.477992	−	0.878364i	$-0.341365\pi$
$223$	−1.58284	−	0.994562i	−0.105995	−	0.0666008i	−0.583986	+	0.811764i	$0.698508\pi$
$224$	9.60897	+	18.8195i	0.642027	+	1.25743i
$225$	−0.536219	−	4.33565i	−0.0357479	−	0.289044i
$226$	−5.08248	−	8.80312i	−0.338082	−	0.585575i
$227$	2.37639	−	0.636753i	0.157727	−	0.0422628i	−0.179092	−	0.983832i	$-0.557316\pi$
$227$	2.37639	−	0.636753i	0.157727	−	0.0422628i	0.336818	+	0.941570i	$0.390649\pi$
$228$	0.682443	+	18.2387i	0.0451959	+	1.20789i
$229$	−15.6269	−	10.6542i	−1.03265	−	0.704052i	−0.0765460	−	0.997066i	$-0.524389\pi$
$229$	−15.6269	−	10.6542i	−1.03265	−	0.704052i	−0.956108	+	0.293014i	$0.905342\pi$
$230$	21.3973	−	1.31815i	1.41090	−	0.0869165i
$231$	0.770787	+	1.07584i	0.0507140	+	0.0707853i
$232$	−0.0286942	−	0.254668i	−0.00188387	−	0.0167198i
$233$	−13.3382	−	7.04943i	−0.873813	−	0.461824i	−0.0306804	−	0.999529i	$-0.509767\pi$
$233$	−13.3382	−	7.04943i	−0.873813	−	0.461824i	−0.843133	+	0.537706i	$0.819291\pi$
$234$	1.51479	+	3.85963i	0.0990251	+	0.252312i
$235$	2.18224	+	21.9874i	0.142354	+	1.43430i
$236$	28.6060	+	11.2270i	1.86209	+	0.730817i
$237$	−0.261574	−	0.747535i	−0.0169910	−	0.0485576i
$238$	−9.57232	+	19.1797i	−0.620481	+	1.24323i
$239$	6.93863	+	14.4082i	0.448823	+	0.931990i	0.995510	+	0.0946535i	$0.0301743\pi$
$239$	6.93863	+	14.4082i	0.448823	+	0.931990i	−0.546687	+	0.837337i	$0.684111\pi$
$240$	−12.0737	+	3.06395i	−0.779351	+	0.197777i
$241$	−1.23578	+	4.00629i	−0.0796034	+	0.258068i	−0.986622	−	0.163022i	$-0.947876\pi$
$241$	−1.23578	+	4.00629i	−0.0796034	+	0.258068i	0.907019	+	0.421089i	$0.138352\pi$
$242$	4.29971	−	22.7245i	0.276396	−	1.46079i
$243$	−7.09293	+	5.23482i	−0.455012	+	0.335814i
$244$	−24.2317			−1.55128
$245$	14.7952	−	5.10892i	0.945233	−	0.326397i
$246$	32.5532			2.07552
$247$	−6.76968	+	4.99625i	−0.430744	+	0.317904i
$248$	1.36105	−	7.19334i	0.0864269	−	0.456777i
$249$	−9.54784	+	30.9533i	−0.605070	+	1.96159i
$250$	−13.2728	−	19.5692i	−0.839444	−	1.23767i
$251$	11.5533	+	23.9906i	0.729236	+	1.51427i	0.852970	+	0.521959i	$0.174799\pi$
$251$	11.5533	+	23.9906i	0.729236	+	1.51427i	−0.123734	+	0.992315i	$0.539487\pi$
$252$	−5.55490	−	1.35065i	−0.349926	−	0.0850831i
$253$	−0.380520	−	1.08746i	−0.0239231	−	0.0683683i
$254$	−40.0628	−	15.7235i	−2.51376	−	0.986578i
$255$	−13.0405	−	10.6857i	−0.816626	−	0.669162i
$256$	2.19559	+	5.59427i	0.137224	+	0.349642i
$257$	−15.5531	−	8.22006i	−0.970177	−	0.512753i	−0.0944337	−	0.995531i	$-0.530104\pi$
$257$	−15.5531	−	8.22006i	−0.970177	−	0.512753i	−0.875743	+	0.482778i	$0.839628\pi$
$258$	−0.117337	−	1.04139i	−0.00730507	−	0.0648343i
$259$	1.65952	+	0.0855710i	0.103118	+	0.00531712i
$260$	9.29619	+	8.21729i	0.576525	+	0.509615i
$261$	−0.184956	−	0.126101i	−0.0114485	−	0.00780544i
$262$	0.641237	+	17.1374i	0.0396158	+	1.05875i
$263$	−4.46607	+	1.19668i	−0.275390	+	0.0737904i	−0.393871	−	0.919166i	$-0.628864\pi$
$263$	−4.46607	+	1.19668i	−0.275390	+	0.0737904i	0.118481	+	0.992956i	$0.462198\pi$
$264$	−0.250187	−	0.433337i	−0.0153979	−	0.0266700i
$265$	−1.23767	+	24.4033i	−0.0760292	+	1.49908i
$266$	−0.488470	−	20.9770i	−0.0299500	−	1.28618i
$267$	−1.06785	−	0.670972i	−0.0653511	−	0.0410628i
$268$	28.1915	+	1.05485i	1.72207	+	0.0644352i
$269$	24.1993	−	3.64746i	1.47546	−	0.222390i	0.638486	−	0.769633i	$-0.279561\pi$
$269$	24.1993	−	3.64746i	1.47546	−	0.222390i	0.836974	+	0.547243i	$0.184323\pi$
$270$	−8.82286	+	17.7154i	−0.536942	+	1.07813i
$271$	20.7513	+	22.3645i	1.26055	+	1.35855i	0.905867	+	0.423562i	$0.139220\pi$
$271$	20.7513	+	22.3645i	1.26055	+	1.35855i	0.354682	+	0.934987i	$0.384589\pi$
$272$	−5.76858	+	9.18065i	−0.349772	+	0.556659i
$273$	−4.11466	−	10.9355i	−0.249030	−	0.661845i
$274$	−36.9990	−	8.44479i	−2.23519	−	0.510168i
$275$	−0.818406	+	0.972147i	−0.0493518	+	0.0586227i
$276$	19.1079	+	11.0320i	1.15016	+	0.664047i
$277$	−15.8395	+	0.592674i	−0.951706	+	0.0356103i	−0.508733	−	0.860925i	$-0.669886\pi$
$277$	−15.8395	+	0.592674i	−0.951706	+	0.0356103i	−0.442973	+	0.896535i	$0.646076\pi$
$278$	7.11346	−	1.34594i	0.426637	−	0.0807241i
$279$	−3.98700	−	4.99954i	−0.238695	−	0.299315i
$280$	−5.75604	+	1.37453i	−0.343989	+	0.0821437i
$281$	1.49322	−	1.87243i	0.0890778	−	0.111700i	−0.735295	−	0.677747i	$-0.762956\pi$
$281$	1.49322	−	1.87243i	0.0890778	−	0.111700i	0.824373	+	0.566047i	$0.191528\pi$
$282$	−19.2197	+	36.3655i	−1.14452	+	2.16553i
$283$	17.5268	+	7.64685i	1.04186	+	0.454558i	0.849955	−	0.526855i	$-0.176629\pi$
$283$	17.5268	+	7.64685i	1.04186	+	0.454558i	0.191904	+	0.981414i	$0.438534\pi$
$284$	25.6320	+	1.92085i	1.52098	+	0.113982i
$285$	16.1731	+	3.28306i	0.958015	+	0.194472i
$286$	0.523293	−	1.08663i	0.0309429	−	0.0642537i
$287$	−20.6889	−	0.292106i	−1.22123	−	0.0172425i
$288$	−6.58663	−	2.30476i	−0.388121	−	0.135809i
$289$	2.31842	−	0.173741i	0.136377	−	0.0102201i
$290$	−1.20209	−	0.151627i	−0.0705892	−	0.00890386i
$291$	0.801028	−	0.546132i	0.0469571	−	0.0320148i
$292$	0.224785	+	0.304572i	0.0131545	+	0.0178237i
$293$	17.7230	−	17.7230i	1.03539	−	1.03539i	0.0360400	−	0.999350i	$-0.488526\pi$
$293$	17.7230	−	17.7230i	1.03539	−	1.03539i	0.999350	−	0.0360400i	$-0.0114744\pi$
$294$	28.2132	+	7.28326i	1.64543	+	0.424769i
$295$	15.9560	−	22.7484i	0.928993	−	1.32446i
$296$	−0.621248	−	0.0936381i	−0.0361093	−	0.00544260i
$297$	1.04506	+	0.197736i	0.0606405	+	0.0114738i
$298$	−22.5386	−	42.6452i	−1.30563	−	2.47037i
$299$	0.760100	+	10.1428i	0.0439577	+	0.586575i
$300$	−0.264094	−	24.3348i	−0.0152475	−	1.40497i
$301$	0.0652276	+	0.662900i	0.00375966	+	0.0382089i
$302$	18.0008	−	6.29873i	1.03583	−	0.362451i
$303$	−1.82894	+	0.797958i	−0.105070	+	0.0458415i
$304$	0.793140	−	10.5837i	0.0454897	−	0.607018i
$305$	−5.15863	+	21.2945i	−0.295382	+	1.21932i
$306$	−2.08656	−	6.76446i	−0.119281	−	0.386698i
$307$	−6.02366	+	0.678704i	−0.343789	+	0.0387357i	−0.282171	−	0.959364i	$-0.591055\pi$
$307$	−6.02366	+	0.678704i	−0.343789	+	0.0387357i	−0.0616177	+	0.998100i	$0.519626\pi$
$308$	0.811035	+	1.45171i	0.0462130	+	0.0827186i
$309$	15.6921	−	12.5140i	0.892693	−	0.711899i
$310$	−31.5370	−	14.2607i	−1.79118	−	0.809952i
$311$	−1.01401	+	1.09284i	−0.0574990	+	0.0619692i	−0.761146	−	0.648580i	$-0.775363\pi$
$311$	−1.01401	+	1.09284i	−0.0574990	+	0.0619692i	0.703647	+	0.710549i	$0.251554\pi$
$312$	1.14333	+	4.26695i	0.0647280	+	0.241568i
$313$	7.63321	+	2.04531i	0.431454	+	0.115608i	0.468009	−	0.883724i	$-0.344972\pi$
$313$	7.63321	+	2.04531i	0.431454	+	0.115608i	−0.0365544	+	0.999332i	$0.511638\pi$
$314$	3.08990	−	13.5377i	0.174373	−	0.763978i
$315$	−2.36950	+	4.59402i	−0.133506	+	0.258844i
$316$	−0.221431	−	0.970152i	−0.0124565	−	0.0545753i
$317$	0.560186	−	14.9713i	0.0314632	−	0.840871i	−0.890820	−	0.454356i	$-0.849869\pi$
$317$	0.560186	−	14.9713i	0.0314632	−	0.840871i	0.922283	−	0.386515i	$-0.126321\pi$
$318$	−27.0109	+	36.5984i	−1.51470	+	2.05234i
$319$	0.00970484	+	0.0643874i	0.000543367	+	0.00360500i
$320$	−24.8793	+	3.41286i	−1.39080	+	0.190785i
$321$	11.3645	−	2.59388i	0.634305	−	0.144776i
$322$	−21.7861	−	12.9917i	−1.21409	−	0.723999i
$323$	12.1631	−	7.64260i	0.676775	−	0.425246i
$324$	−23.2537	+	13.4255i	−1.29187	+	0.745861i
$325$	9.20027	−	6.41999i	0.510339	−	0.356117i
$326$	−18.5171	−	17.1814i	−1.02557	−	0.951588i
$327$	3.59693	+	19.0102i	0.198910	+	1.05127i
$328$	7.77363	+	0.875878i	0.429227	+	0.0483623i
$329$	12.5412	−	22.9392i	0.691419	−	1.26468i
$330$	−2.26958	+	0.667213i	−0.124936	+	0.0367289i
$331$	−14.4883	+	4.46904i	−0.796348	+	0.245641i	−0.666121	−	0.745843i	$-0.732047\pi$
$331$	−14.4883	+	4.46904i	−0.796348	+	0.245641i	−0.130227	+	0.991484i	$0.541570\pi$
$332$	−16.2757	+	37.3043i	−0.893246	+	2.04734i
$333$	−0.415953	+	0.357957i	−0.0227941	+	0.0196159i
$334$	19.2961	−	49.1657i	1.05584	−	2.69023i
$335$	6.92859	−	24.5497i	0.378550	−	1.34129i
$336$	13.8414	+	5.06375i	0.755109	+	0.276250i
$337$	−1.49765	+	4.28004i	−0.0815821	+	0.233148i	−0.977448	−	0.211176i	$-0.932271\pi$
$337$	−1.49765	+	4.28004i	−0.0815821	+	0.233148i	0.895866	+	0.444325i	$0.146556\pi$
$338$	10.9889	−	12.7693i	0.597715	−	0.694558i
$339$	−9.03934	−	2.78827i	−0.490950	−	0.151438i
$340$	−14.7787	−	15.1764i	−0.801489	−	0.823055i
$341$	−0.277232	+	1.83931i	−0.0150129	+	0.0996043i
$342$	4.89978	+	4.89978i	0.264950	+	0.264950i
$343$	−17.8652	−	4.88197i	−0.964632	−	0.263601i
$344$		−	0.251839i		−	0.0135783i
$345$	13.7626	−	14.4432i	0.740952	−	0.777596i
$346$	16.0484	+	23.5387i	0.862768	+	1.26545i
$347$	−1.37891	+	0.728776i	−0.0740239	+	0.0391227i	−0.503871	−	0.863779i	$-0.668091\pi$
$347$	−1.37891	+	0.728776i	−0.0740239	+	0.0391227i	0.429847	+	0.902902i	$0.358567\pi$
$348$	−0.945189	−	0.813401i	−0.0506675	−	0.0436029i
$349$	−12.0645	+	5.80994i	−0.645796	+	0.310999i	−0.727960	−	0.685620i	$-0.759531\pi$
$349$	−12.0645	+	5.80994i	−0.645796	+	0.310999i	0.0821637	+	0.996619i	$0.473817\pi$
$350$	−0.0913761	+	27.9779i	−0.00488426	+	1.49548i
$351$	−8.45995	−	4.07410i	−0.451559	−	0.217459i
$352$	0.811717	+	1.86047i	0.0432646	+	0.0991636i
$353$	0.847137	+	0.984391i	0.0450886	+	0.0523939i	0.780063	−	0.625701i	$-0.215187\pi$
$353$	0.847137	+	0.984391i	0.0450886	+	0.0523939i	−0.734975	+	0.678095i	$0.762806\pi$
$354$	48.1505	−	18.8977i	2.55917	−	1.00440i
$355$	7.14475	−	22.1161i	0.379204	−	1.17380i
$356$	−1.23889	−	0.987984i	−0.0656612	−	0.0523630i
$357$	5.61015	+	19.1431i	0.296921	+	1.01316i
$358$	1.80021	−	15.9773i	0.0951441	−	0.844427i
$359$	−12.0560	+	17.6830i	−0.636293	+	0.933271i	0.363705	+	0.931514i	$0.381512\pi$
$359$	−12.0560	+	17.6830i	−0.636293	+	0.933271i	−0.999998	+	0.00175691i	$0.999441\pi$
$360$	1.06164	−	1.64083i	0.0559534	−	0.0864795i
$361$	2.46934	−	4.27702i	0.129965	−	0.225106i
$362$	−12.2962	+	45.8901i	−0.646274	+	2.41193i
$363$	−11.4509	−	18.2239i	−0.601014	−	0.956508i
$364$	−3.59905	−	14.2326i	−0.188641	−	0.745991i
$365$	0.315507	−	0.132698i	0.0165144	−	0.00694571i
$366$	−29.8994	+	27.7426i	−1.56287	+	1.45013i
$367$	−13.3531	−	9.85501i	−0.697024	−	0.514427i	0.186711	−	0.982415i	$-0.440217\pi$
$367$	−13.3531	−	9.85501i	−0.697024	−	0.514427i	−0.883735	+	0.467988i	$0.844979\pi$
$368$	−10.3233	−	7.61896i	−0.538140	−	0.397166i
$369$	5.00895	−	4.64763i	0.260755	−	0.241946i
$370$	−1.12176	+	2.75028i	−0.0583176	+	0.142980i
$371$	17.4949	−	23.0174i	0.908289	−	1.19500i
$372$	−18.9521	−	30.1621i	−0.982622	−	1.56383i
$373$	−5.84262	+	21.8050i	−0.302519	+	1.12902i	0.632540	+	0.774527i	$0.282012\pi$
$373$	−5.84262	+	21.8050i	−0.302519	+	1.12902i	−0.935060	+	0.354490i	$0.884654\pi$
$374$	−1.02957	+	1.78327i	−0.0532378	+	0.0922105i
$375$	−21.4413	−	4.94850i	−1.10722	−	0.255539i
$376$	−5.56807	+	8.16686i	−0.287151	+	0.421174i
$377$	0.0643633	−	0.571240i	0.00331488	−	0.0294203i
$378$	20.4429	−	11.4210i	1.05147	−	0.587432i
$379$	4.59144	+	3.66155i	0.235847	+	0.188081i	0.734280	−	0.678846i	$-0.237520\pi$
$379$	4.59144	+	3.66155i	0.235847	+	0.188081i	−0.498434	+	0.866928i	$0.666091\pi$
$380$	19.7315	+	6.37440i	1.01221	+	0.327000i
$381$	−37.2827	+	14.6324i	−1.91005	+	0.749641i
$382$	−22.7115	−	26.3913i	−1.16202	−	1.35030i
$383$	−10.4401	−	23.9290i	−0.533465	−	1.22272i	−0.949615	−	0.313419i	$-0.898526\pi$
$383$	−10.4401	−	23.9290i	−0.533465	−	1.22272i	0.416150	−	0.909296i	$-0.363379\pi$
$384$	−13.7937	−	6.64269i	−0.703906	−	0.338983i
$385$	1.44840	−	0.403675i	0.0738171	−	0.0205732i
$386$	16.9576	−	8.16635i	0.863119	−	0.415656i
$387$	−0.166734	−	0.143486i	−0.00847558	−	0.00729383i
$388$	1.07697	−	0.569197i	0.0546751	−	0.0288966i
$389$	−17.1013	−	25.0830i	−0.867069	−	1.27176i	−0.961104	−	0.276188i	$-0.910929\pi$
$389$	−17.1013	−	25.0830i	−0.867069	−	1.27176i	0.0940344	−	0.995569i	$-0.470024\pi$
$390$	20.8784	−	0.503811i	1.05722	−	0.0255114i
$391$		−	17.3656i		−	0.878216i
$392$	6.54127	+	2.49833i	0.330384	+	0.126185i
$393$	11.2850	+	11.2850i	0.569253	+	0.569253i
$394$	3.10724	−	20.6152i	0.156541	−	1.03858i
$395$	−0.899694	−	0.0119432i	−0.0452685	−	0.000600926i
$396$	−0.524760	−	0.161867i	−0.0263702	−	0.00813413i
$397$	−8.40447	+	9.76618i	−0.421808	+	0.490150i	−0.928162	−	0.372175i	$-0.878612\pi$
$397$	−8.40447	+	9.76618i	−0.421808	+	0.490150i	0.506354	+	0.862326i	$0.330993\pi$
$398$	2.81198	−	8.03618i	0.140952	−	0.402817i
$399$	−13.6111	−	14.0010i	−0.681407	−	0.700925i
$400$	−1.43180	+	14.0792i	−0.0715898	+	0.703958i
$401$	−1.72388	+	4.39236i	−0.0860863	+	0.219344i	−0.967434	−	0.253124i	$-0.918542\pi$
$401$	−1.72388	+	4.39236i	−0.0860863	+	0.219344i	0.881347	+	0.472469i	$0.156637\pi$
$402$	35.9930	−	30.9745i	1.79517	−	1.54487i
$403$	6.56682	−	15.0513i	0.327116	−	0.749759i
$404$	−2.39583	+	0.739014i	−0.119197	+	0.0367673i
$405$	6.84771	+	23.2931i	0.340266	+	1.15744i
$406$	1.07332	+	0.950368i	0.0532680	+	0.0471660i
$407$	0.158624	+	0.0178726i	0.00786269	+	0.000885913i
$408$	−1.40215	−	7.41054i	−0.0694167	−	0.366876i
$409$	2.03133	+	1.88480i	0.100443	+	0.0931972i	0.728796	−	0.684731i	$-0.240080\pi$
$409$	2.03133	+	1.88480i	0.100443	+	0.0931972i	−0.628353	+	0.777928i	$0.716271\pi$
$410$	12.6773	−	34.7434i	0.626089	−	1.71585i
$411$	−30.5855	+	17.6585i	−1.50867	+	0.871032i
$412$	21.3533	−	13.4171i	1.05200	−	0.661015i
$413$	−30.7711	+	11.5782i	−1.51415	+	0.569724i
$414$	8.16678	−	1.86401i	0.401375	−	0.0916113i
$415$	29.3176	+	22.2445i	1.43914	+	1.09194i
$416$	−2.67085	−	17.7199i	−0.130949	−	0.868792i
$417$	4.00075	−	5.42082i	0.195917	−	0.265459i
$418$	0.0753664	−	2.01421i	0.00368629	−	0.0985182i
$419$	1.78701	+	7.82938i	0.0873010	+	0.382490i	0.999637	−	0.0269524i	$-0.00858025\pi$
$419$	1.78701	+	7.82938i	0.0873010	+	0.382490i	−0.912336	+	0.409443i	$0.865723\pi$
$420$	−15.9819	+	23.9527i	−0.779838	+	1.16877i
$421$	7.55555	−	33.1030i	0.368235	−	1.61334i	−0.363391	−	0.931637i	$-0.618381\pi$
$421$	7.55555	−	33.1030i	0.368235	−	1.61334i	0.731626	−	0.681706i	$-0.238762\pi$
$422$	22.5032	+	6.02970i	1.09544	+	0.293521i
$423$	2.23457	+	8.33954i	0.108649	+	0.405482i
$424$	−7.43485	+	8.01286i	−0.361068	+	0.389139i
$425$	−16.4830	+	9.75646i	−0.799542	+	0.473258i
$426$	33.8264	−	26.9757i	1.63890	−	1.30698i
$427$	19.2512	−	17.3632i	0.931632	−	0.840266i
$428$	14.5543	−	1.63988i	0.703511	−	0.0792666i
$429$	−0.330826	−	1.07251i	−0.0159724	−	0.0517814i
$430$	−1.15715	−	0.280323i	−0.0558028	−	0.0135184i
$431$	−2.26007	+	30.1585i	−0.108864	+	1.45268i	0.628827	+	0.777545i	$0.283535\pi$
$431$	−2.26007	+	30.1585i	−0.108864	+	1.45268i	−0.737691	+	0.675139i	$0.764084\pi$
$432$	10.8564	−	4.73659i	0.522328	−	0.227889i
$433$	17.8990	−	6.26312i	0.860170	−	0.300987i	0.136085	−	0.990697i	$-0.456548\pi$
$433$	17.8990	−	6.26312i	0.860170	−	0.300987i	0.724085	+	0.689711i	$0.242262\pi$
$434$	21.2965	+	34.9798i	1.02226	+	1.67909i
$435$	−0.916023	+	0.657455i	−0.0439200	+	0.0315225i
$436$	1.81666	+	24.2417i	0.0870024	+	1.16097i
$437$	7.94290	+	15.0287i	0.379960	+	0.718920i
$438$	0.626063	+	0.118457i	0.0299144	+	0.00566011i
$439$	4.16027	+	0.627060i	0.198559	+	0.0299279i	0.247569	−	0.968870i	$-0.420368\pi$
$439$	4.16027	+	0.627060i	0.198559	+	0.0299279i	−0.0490097	+	0.998798i	$0.515607\pi$
$440$	−0.559922	+	0.0982634i	−0.0266933	+	0.00468452i
$441$	5.38098	−	2.90732i	0.256237	−	0.138444i
$442$	12.8543	−	12.8543i	0.611418	−	0.611418i
$443$	22.3378	+	30.2666i	1.06130	+	1.43801i	0.891773	+	0.452484i	$0.149462\pi$
$443$	22.3378	+	30.2666i	1.06130	+	1.43801i	0.169527	+	0.985526i	$0.445776\pi$
$444$	−2.52581	+	1.72207i	−0.119870	+	0.0817257i
$445$	−1.13197	+	0.878390i	−0.0536605	+	0.0416397i
$446$	−3.94254	+	0.295452i	−0.186685	+	0.0139901i
$447$	−42.3688	−	14.8255i	−2.00398	−	0.701221i
$448$	26.5861	+	13.2688i	1.25607	+	0.626890i
$449$	−1.09417	+	2.27207i	−0.0516372	+	0.107226i	−0.925191	−	0.379502i	$-0.876095\pi$
$449$	−1.09417	+	2.27207i	−0.0516372	+	0.107226i	0.873554	+	0.486728i	$0.161810\pi$
$450$	−6.35759	−	6.70444i	−0.299700	−	0.316050i
$451$	−1.98204	−	0.148533i	−0.0933306	−	0.00699416i
$452$	−10.8940	−	4.75302i	−0.512413	−	0.223563i
$453$	8.29289	−	15.6909i	0.389634	−	0.737224i
$454$	3.24416	−	4.06805i	0.152256	−	0.190923i
$455$	−13.2736	+	0.132845i	−0.622275	+	0.00622789i
$456$	4.60299	+	5.77196i	0.215555	+	0.270297i
$457$	18.8896	−	3.57411i	0.883619	−	0.167190i	0.275752	−	0.961229i	$-0.411073\pi$
$457$	18.8896	−	3.57411i	0.883619	−	0.167190i	0.607867	+	0.794039i	$0.292025\pi$
$458$	−39.9725	+	1.49567i	−1.86779	+	0.0698878i
$459$	13.8836	+	8.01572i	0.648032	+	0.374142i
$460$	19.2155	−	16.0973i	0.895926	−	0.750540i
$461$	−26.0978	−	5.95665i	−1.21549	−	0.277429i	−0.433753	−	0.901032i	$-0.642811\pi$
$461$	−26.0978	−	5.95665i	−1.21549	−	0.277429i	−0.781741	+	0.623603i	$0.785668\pi$
$462$	2.66277	+	0.862710i	0.123883	+	0.0401369i
$463$	−16.2502	+	25.8620i	−0.755209	+	1.20191i	0.218881	+	0.975751i	$0.429759\pi$
$463$	−16.2502	+	25.8620i	−0.755209	+	1.20191i	−0.974091	+	0.226157i	$0.927384\pi$
$464$	0.493222	+	0.531567i	0.0228972	+	0.0246774i
$465$	−30.5407	+	10.2337i	−1.41629	+	0.474576i
$466$	−31.5506	+	4.75549i	−1.46155	+	0.220294i
$467$	−42.7069	−	1.59798i	−1.97624	−	0.0739456i	−0.982541	−	0.186047i	$-0.940432\pi$
$467$	−42.7069	−	1.59798i	−1.97624	−	0.0739456i	−0.993697	+	0.112101i	$0.964242\pi$
$468$	4.10504	+	2.57937i	0.189756	+	0.119231i
$469$	−23.1529	+	19.3626i	−1.06910	+	0.894080i
$470$	31.3273	+	34.6747i	1.44502	+	1.59943i
$471$	−6.46116	−	11.1911i	−0.297714	−	0.515657i
$472$	12.0067	−	3.21718i	0.552652	−	0.148083i
$473$	0.00239253	+	0.0639418i	0.000110009	+	0.00294004i
$474$	−1.38394	−	0.943554i	−0.0635664	−	0.0433389i
$475$	9.80232	−	15.9827i	0.449761	−	0.733338i
$476$	4.31163	+	24.6908i	0.197623	+	1.13170i
$477$	1.06901	+	9.48773i	0.0489466	+	0.434413i
$478$	29.9025	+	15.8039i	1.36771	+	0.722855i
$479$	7.94706	+	20.2488i	0.363110	+	0.925190i	0.989350	+	0.145559i	$0.0464981\pi$
$479$	7.94706	+	20.2488i	0.363110	+	0.925190i	−0.626239	+	0.779631i	$0.715407\pi$
$480$	−22.2780	+	27.1874i	−1.01684	+	1.24093i
$481$	−1.31183	−	0.514855i	−0.0598143	−	0.0234754i
$482$	2.92858	+	8.36941i	0.133393	+	0.381216i
$483$	−23.0855	+	4.92730i	−1.05043	+	0.224200i
$484$	−11.7335	−	24.3648i	−0.533341	−	1.10749i
$485$	−0.270928	−	1.06760i	−0.0123022	−	0.0484774i
$486$	−5.49549	+	17.8159i	−0.249280	+	0.808147i
$487$	2.65250	−	14.0188i	0.120196	−	0.635252i	−0.869714	−	0.493556i	$-0.835697\pi$
$487$	2.65250	−	14.0188i	0.120196	−	0.635252i	0.989910	−	0.141696i	$-0.0452556\pi$
$488$	−7.88636	+	5.82040i	−0.356999	+	0.263477i
$489$	−23.5075			−1.06304
$490$	18.7604	−	27.2750i	0.847510	−	1.23216i
$491$	−14.5681			−0.657448			−0.328724	−	0.944426i	$-0.606619\pi$
$491$	−14.5681			−0.657448			−0.328724	+	0.944426i	$0.606619\pi$
$492$	30.6263	−	22.6032i	1.38074	−	1.01903i
$493$	−0.182465	+	0.964348i	−0.00821779	+	0.0434321i
$494$	−5.24504	+	17.0040i	−0.235985	+	0.765046i
$495$	−0.253961	+	0.426692i	−0.0114147	+	0.0191784i
$496$	8.98774	+	18.6632i	0.403562	+	0.838004i
$497$	−21.7401	+	16.8406i	−0.975176	+	0.755403i
$498$	22.6268	+	64.6636i	1.01393	+	2.89765i
$499$	2.28791	+	0.897938i	0.102421	+	0.0401972i	0.415998	−	0.909365i	$-0.363432\pi$
$499$	2.28791	+	0.897938i	0.102421	+	0.0401972i	−0.313577	+	0.949563i	$0.601527\pi$
$500$	−26.0749	−	9.19495i	−1.16611	−	0.411211i
$501$	−17.9571	−	45.7540i	−0.802265	−	2.04414i
$502$	49.7896	+	26.3146i	2.22222	+	1.17448i
$503$	−0.314843	−	2.79431i	−0.0140382	−	0.124592i	0.984739	−	0.174040i	$-0.0556823\pi$
$503$	−0.314843	−	2.79431i	−0.0140382	−	0.124592i	−0.998777	+	0.0494482i	$0.984254\pi$
$504$	−2.13230	+	0.894695i	−0.0949801	+	0.0398529i
$505$	0.139393	+	2.26274i	0.00620291	+	0.100691i
$506$	−2.01326	−	1.37262i	−0.0895004	−	0.0610203i
$507$	−0.586206	−	15.6667i	−0.0260343	−	0.695782i
$508$	−48.6088	+	13.0247i	−2.15667	+	0.577877i
$509$	0.831483	+	1.44017i	0.0368548	+	0.0638344i	0.883864	−	0.467743i	$-0.154933\pi$
$509$	0.831483	+	1.44017i	0.0368548	+	0.0638344i	−0.847010	+	0.531578i	$0.821599\pi$
$510$	−35.6107	−	1.80608i	−1.57687	−	0.0799744i
$511$	−0.396825	−	0.0809022i	−0.0175545	−	0.00357890i
$512$	23.9348	+	15.0392i	1.05778	+	0.664646i
$513$	−15.6816	−	0.586765i	−0.692361	−	0.0259063i
$514$	−36.7899	+	5.54518i	−1.62273	+	0.244588i
$515$	−7.24493	−	21.6212i	−0.319250	−	0.952746i
$516$	−0.833478	−	0.898276i	−0.0366918	−	0.0395444i
$517$	1.33614	−	2.12646i	0.0587634	−	0.0935214i
$518$	2.93144	−	1.93857i	0.128800	−	0.0851759i
$519$	25.8474	+	5.89949i	1.13457	+	0.258959i
$520$	4.99927	+	0.441447i	0.219233	+	0.0193587i
$521$	6.65506	+	3.84230i	0.291564	+	0.168334i	0.638647	−	0.769500i	$-0.279495\pi$
$521$	6.65506	+	3.84230i	0.291564	+	0.168334i	−0.347083	+	0.937834i	$0.612828\pi$
$522$	−0.473104	+	0.0177023i	−0.0207072	+	0.000774809i
$523$	11.2556	−	2.12968i	0.492174	−	0.0931244i	0.0661009	−	0.997813i	$-0.478944\pi$
$523$	11.2556	−	2.12968i	0.492174	−	0.0931244i	0.426074	+	0.904689i	$0.359896\pi$
$524$	12.5026	+	15.6777i	0.546178	+	0.684886i
$525$	17.6469	+	19.1439i	0.770176	+	0.835509i
$526$	−6.09690	+	7.64527i	−0.265837	+	0.333350i
$527$	−13.1007	+	24.7876i	−0.570673	+	1.07977i
$528$	1.29767	+	0.566169i	0.0564740	+	0.0246394i
$529$	−2.44377	−	0.183135i	−0.106251	−	0.00796240i
$530$	28.5418	+	43.0808i	1.23978	+	1.87131i
$531$	4.71087	−	9.78222i	0.204434	−	0.424512i
$532$	−15.0248	−	19.3961i	−0.651408	−	0.840926i
$533$	16.5625	+	5.79546i	0.717401	+	0.251029i
$534$	−2.65980	+	0.199324i	−0.115101	+	0.00862560i
$535$	1.65734	−	13.1392i	0.0716529	−	0.568059i
$536$	9.42845	−	6.42821i	0.407247	−	0.277656i
$537$	−8.88516	−	12.0390i	−0.383423	−	0.519520i
$538$	36.5986	−	36.5986i	1.57788	−	1.57788i
$539$	−1.68456	−	0.572180i	−0.0725590	−	0.0246455i
$540$	4.00003	+	22.7929i	0.172134	+	0.980849i
$541$	−1.62033	−	0.244226i	−0.0696636	−	0.0105001i	0.114118	−	0.993467i	$-0.463596\pi$
$541$	−1.62033	−	0.244226i	−0.0696636	−	0.0105001i	−0.183782	+	0.982967i	$0.558834\pi$
$542$	63.3994	+	11.9958i	2.72324	+	0.515264i
$543$	20.6590	+	39.0887i	0.886561	+	1.67746i
$544$	2.28639	+	30.5097i	0.0980281	+	1.30809i
$545$	21.6900	+	3.56429i	0.929096	+	0.152678i
$546$	−20.7356	−	13.4411i	−0.887402	−	0.575224i
$547$	0.128578	−	0.0449914i	0.00549760	−	0.00192369i	−0.327529	−	0.944841i	$-0.606216\pi$
$547$	0.128578	−	0.0449914i	0.00549760	−	0.00192369i	0.333026	+	0.942917i	$0.391930\pi$
$548$	−40.6725	+	17.7452i	−1.73744	+	0.758039i
$549$	−0.639796	+	8.53749i	−0.0273058	+	0.364371i
$550$	−0.171749	+	2.68211i	−0.00732341	+	0.114366i
$551$	−0.283176	−	0.918034i	−0.0120637	−	0.0391095i
$552$	8.86865	−	0.999257i	0.377475	−	0.0425312i
$553$	0.871081	+	0.612084i	0.0370421	+	0.0260285i
$554$	−26.2094	+	20.9013i	−1.11353	+	0.888012i
$555$	0.975613	+	2.58625i	0.0414125	+	0.109780i
$556$	5.75784	−	6.20547i	0.244187	−	0.263171i
$557$	9.51999	+	35.5291i	0.403375	+	1.50542i	0.807034	+	0.590506i	$0.201072\pi$
$557$	9.51999	+	35.5291i	0.403375	+	1.50542i	−0.403659	+	0.914910i	$0.632262\pi$
$558$	−13.0635	−	3.50035i	−0.553021	−	0.148182i
$559$	0.125701	−	0.550731i	0.00531658	−	0.0232934i
$560$	10.7947	−	12.8006i	0.456161	−	0.540925i
$561$	0.426406	+	1.86821i	0.0180029	+	0.0788758i
$562$	0.189392	−	5.06159i	0.00798900	−	0.213510i
$563$	5.38306	−	7.29379i	0.226869	−	0.307396i	−0.676347	−	0.736583i	$-0.736438\pi$
$563$	5.38306	−	7.29379i	0.226869	−	0.307396i	0.903216	+	0.429187i	$0.141200\pi$
$564$	7.16821	+	47.5580i	0.301836	+	2.00255i
$565$	−6.49609	+	8.56165i	−0.273292	+	0.360192i
$566$	39.4285	−	8.99931i	1.65730	−	0.378269i
$567$	8.85413	−	27.3285i	0.371839	−	1.14769i
$568$	8.80347	−	5.53159i	0.369386	−	0.232100i
$569$	−7.69748	+	4.44414i	−0.322695	+	0.186308i	−0.652593	−	0.757708i	$-0.726319\pi$
$569$	−7.69748	+	4.44414i	−0.322695	+	0.186308i	0.329898	+	0.944017i	$0.392986\pi$
$570$	31.6446	−	14.7250i	1.32545	−	0.616764i
$571$	7.96417	+	7.38967i	0.333290	+	0.309248i	0.829009	−	0.559235i	$-0.188905\pi$
$571$	7.96417	+	7.38967i	0.333290	+	0.309248i	−0.495719	+	0.868483i	$0.665095\pi$
$572$	−0.262180	−	1.38565i	−0.0109623	−	0.0579370i
$573$	−32.1985	−	3.62790i	−1.34511	−	0.151558i
$574$	−35.5726	+	25.4860i	−1.48477	+	1.06376i
$575$	−10.0553	−	20.3132i	−0.419335	−	0.847118i
$576$	−9.37661	+	2.89230i	−0.390692	+	0.120513i
$577$	12.2952	−	28.1810i	0.511858	−	1.17319i	−0.448338	−	0.893864i	$-0.647984\pi$
$577$	12.2952	−	28.1810i	0.511858	−	1.17319i	0.960196	−	0.279327i	$-0.0901112\pi$
$578$	3.72699	−	3.20734i	0.155022	−	0.133408i
$579$	6.39912	−	16.3047i	0.265938	−	0.677599i
$580$	−1.23621	+	0.692015i	−0.0513310	+	0.0287344i
$581$	−13.8000	−	41.2993i	−0.572519	−	1.71338i
$582$	0.677207	−	1.93535i	0.0280711	−	0.0802227i
$583$	1.81158	−	2.10509i	0.0750279	−	0.0871840i
$584$	0.146315	+	0.0451322i	0.00605456	+	0.00186758i
$585$	3.14062	−	3.05833i	0.129849	−	0.126447i
$586$	7.90061	−	52.4171i	0.326371	−	2.16533i
$587$	16.0460	+	16.0460i	0.662289	+	0.662289i	0.955919	−	0.293630i	$-0.0948634\pi$
$587$	16.0460	+	16.0460i	0.662289	+	0.662289i	−0.293630	+	0.955919i	$0.594863\pi$
$588$	31.6002	−	12.7376i	1.30317	−	0.525288i
$589$		−	27.4441i		−	1.13081i
$590$	−1.41766	−	58.7494i	−0.0583643	−	2.41868i
$591$	−10.9292	−	16.0302i	−0.449567	−	0.659394i
$592$	1.57167	−	0.830651i	0.0645952	−	0.0341395i
$593$	−11.0998	−	9.55218i	−0.455815	−	0.392261i	0.394195	−	0.919027i	$-0.371023\pi$
$593$	−11.0998	−	9.55218i	−0.455815	−	0.392261i	−0.850010	+	0.526766i	$0.823404\pi$
$594$	2.02669	−	0.976002i	0.0831561	−	0.0400458i
$595$	22.6158	+	1.46738i	0.927158	+	0.0601565i
$596$	−50.8150	−	24.4712i	−2.08146	−	1.00238i
$597$	−3.16841	−	7.26207i	−0.129674	−	0.297217i
$598$	14.0318	+	16.3052i	0.573802	+	0.666770i
$599$	40.8497	−	16.0323i	1.66907	−	0.655063i	0.672681	−	0.739933i	$-0.265143\pi$
$599$	40.8497	−	16.0323i	1.66907	−	0.655063i	0.996392	+	0.0848703i	$0.0270476\pi$
$600$	−5.93112	−	7.85648i	−0.242137	−	0.320740i
$601$	0.954511	+	0.761197i	0.0389353	+	0.0310499i	0.642764	−	0.766064i	$-0.277788\pi$
$601$	0.954511	+	0.761197i	0.0389353	+	0.0310499i	−0.603829	+	0.797114i	$0.706359\pi$
$602$	0.943528	+	1.04612i	0.0384553	+	0.0426367i
$603$	1.11600	−	9.90476i	0.0454470	−	0.403353i
$604$	12.5617	−	18.4246i	0.511128	−	0.749688i
$605$	−23.9094	+	5.12424i	−0.972054	+	0.208330i
$606$	−2.11011	+	3.65482i	−0.0857175	+	0.148467i
$607$	5.76509	−	21.5156i	0.233998	−	0.873291i	−0.744601	−	0.667510i	$-0.767360\pi$
$607$	5.76509	−	21.5156i	0.233998	−	0.873291i	0.978598	−	0.205781i	$-0.0659733\pi$
$608$	−15.9336	−	25.3583i	−0.646195	−	1.02841i
$609$	1.33376	−	0.0310580i	0.0540467	−	0.00125853i
$610$	17.9653	+	42.7150i	0.727392	+	1.72948i
$611$	−16.2528	+	15.0804i	−0.657518	+	0.610087i
$612$	−6.65992	−	4.91524i	−0.269211	−	0.198687i
$613$	−11.3044	−	8.34300i	−0.456579	−	0.336971i	0.341127	−	0.940017i	$-0.389191\pi$
$613$	−11.3044	−	8.34300i	−0.456579	−	0.336971i	−0.797706	+	0.603047i	$0.793953\pi$
$614$	−9.39795	+	8.72002i	−0.379270	+	0.351911i
$615$	−13.3434	−	31.7258i	−0.538058	−	1.27931i
$616$	0.612652	+	0.277658i	0.0246845	+	0.0111871i
$617$	6.50846	+	10.3582i	0.262021	+	0.417003i	0.951662	−	0.307148i	$-0.0993746\pi$
$617$	6.50846	+	10.3582i	0.262021	+	0.417003i	−0.689641	+	0.724151i	$0.742232\pi$
$618$	10.9866	−	41.0025i	0.441945	−	1.64936i
$619$	13.6782	−	23.6914i	0.549774	−	0.952236i	−0.448516	−	0.893775i	$-0.648047\pi$
$619$	13.6782	−	23.6914i	0.549774	−	0.952236i	0.998290	−	0.0584613i	$-0.0186194\pi$
$620$	−39.5720	+	8.48105i	−1.58925	+	0.340607i
$621$	−10.6865	+	15.6743i	−0.428836	+	0.628986i
$622$	−0.353020	+	3.13314i	−0.0141548	+	0.125627i
$623$	1.69220	−	0.102812i	0.0677964	−	0.00411906i
$624$	−9.77227	−	7.79313i	−0.391204	−	0.311975i
$625$	−13.6314	+	20.9567i	−0.545256	+	0.838270i
$626$	15.5579	−	6.10604i	0.621820	−	0.244047i
$627$	−1.22353	−	1.42177i	−0.0488631	−	0.0567799i
$628$	−6.49288	−	14.8818i	−0.259094	−	0.593850i
$629$	2.16776	+	1.04394i	0.0864342	+	0.0416245i
$630$	1.73748	+	10.7934i	0.0692230	+	0.430019i
$631$	16.0211	−	7.71537i	0.637791	−	0.307144i	−0.0869010	−	0.996217i	$-0.527696\pi$
$631$	16.0211	−	7.71537i	0.637791	−	0.307144i	0.724692	+	0.689073i	$0.241982\pi$
$632$	−0.305094	−	0.262555i	−0.0121360	−	0.0104439i
$633$	19.1680	−	10.1306i	0.761858	−	0.402654i
$634$	−17.8491	−	26.1798i	−0.708878	−	1.03973i
$635$	1.09769	+	45.4894i	0.0435605	+	1.80519i
$636$			53.1869i			2.10900i
$637$	13.0577	+	8.72839i	0.517365	+	0.345831i
$638$	0.0973783	+	0.0973783i	0.00385524	+	0.00385524i
$639$	1.35354	−	8.98013i	0.0535451	−	0.355248i
$640$	−12.4613	+	12.1348i	−0.492577	+	0.479671i
$641$	24.2745	+	7.48768i	0.958784	+	0.295746i	0.734371	−	0.678748i	$-0.237477\pi$
$641$	24.2745	+	7.48768i	0.958784	+	0.295746i	0.224413	+	0.974494i	$0.427953\pi$
$642$	16.0811	−	18.6866i	0.634670	−	0.737500i
$643$	−6.95361	+	19.8723i	−0.274224	+	0.783686i	0.721593	+	0.692317i	$0.243410\pi$
$643$	−6.95361	+	19.8723i	−0.274224	+	0.783686i	−0.995817	+	0.0913693i	$0.970876\pi$
$644$	−29.5172	+	2.90441i	−1.16314	+	0.114450i
$645$	−0.966828	+	0.541216i	−0.0380688	+	0.0213104i
$646$	11.0994	−	28.2808i	0.436700	−	1.11269i
$647$	3.54067	−	3.04699i	0.139198	−	0.119790i	−0.579933	−	0.814664i	$-0.696921\pi$
$647$	3.54067	−	3.04699i	0.139198	−	0.119790i	0.719131	+	0.694875i	$0.244540\pi$
$648$	−4.34327	+	9.95488i	−0.170620	+	0.391065i
$649$	−3.01792	+	0.930906i	−0.118464	+	0.0365412i
$650$	7.59306	−	22.4793i	0.297824	−	0.881711i
$651$	36.6695	+	10.3826i	1.43719	+	0.406925i
$652$	−29.3508	−	3.30704i	−1.14947	−	0.129514i
$653$	5.60056	+	29.5996i	0.219167	+	1.15832i	0.903314	+	0.428980i	$0.141127\pi$
$653$	5.60056	+	29.5996i	0.219167	+	1.15832i	−0.684147	+	0.729344i	$0.739825\pi$
$654$	29.9956	+	27.8319i	1.17292	+	1.08831i
$655$	16.4390	−	7.64948i	0.642325	−	0.298890i
$656$	−19.1692	+	11.0673i	−0.748430	+	0.432106i
$657$	0.113244	−	0.0711560i	0.00441807	−	0.00277606i
$658$	−7.46819	−	54.7856i	−0.291140	−	2.13576i
$659$	2.61922	−	0.597820i	0.102030	−	0.0232878i	−0.171201	−	0.985236i	$-0.554765\pi$
$659$	2.61922	−	0.597820i	0.102030	−	0.0232878i	0.273231	+	0.961948i	$0.411908\pi$
$660$	−1.67196	+	2.20359i	−0.0650808	+	0.0857747i
$661$	−3.56236	−	23.6347i	−0.138560	−	0.919285i	−0.944788	−	0.327681i	$-0.893733\pi$
$661$	−3.56236	−	23.6347i	−0.138560	−	0.919285i	0.806229	−	0.591604i	$-0.201505\pi$
$662$	−19.0417	+	25.8006i	−0.740077	+	1.00277i
$663$	0.632559	−	16.9055i	0.0245665	−	0.656555i
$664$	3.66338	+	16.0503i	0.142167	+	0.622873i
$665$	−20.2436	+	9.07440i	−0.785011	+	0.351890i
$666$	−0.258262	+	1.13152i	−0.0100074	+	0.0438455i
$667$	−1.12182	−	0.300592i	−0.0434372	−	0.0116390i
$668$	−15.9841	−	59.6535i	−0.618444	−	2.30806i
$669$	−2.50252	+	2.69708i	−0.0967532	+	0.104275i
$670$	−19.0415	−	50.4771i	−0.735639	−	1.95010i
$671$	1.94704	−	1.55272i	0.0751648	−	0.0599419i
$672$	39.9104	−	11.6963i	1.53958	−	0.451195i
$673$	−24.4828	+	2.75855i	−0.943742	+	0.106334i	−0.570407	−	0.821362i	$-0.693214\pi$
$673$	−24.4828	+	2.75855i	−0.943742	+	0.106334i	−0.373335	+	0.927696i	$0.621786\pi$
$674$	2.82676	+	9.16412i	0.108883	+	0.352989i
$675$	20.8816	+	1.33715i	0.803733	+	0.0514671i
$676$	1.47208	−	19.6435i	0.0566183	−	0.755519i
$677$	−1.26416	+	0.551546i	−0.0485855	+	0.0211976i	−0.424044	−	0.905641i	$-0.639390\pi$
$677$	−1.26416	+	0.551546i	−0.0485855	+	0.0211976i	0.375459	+	0.926839i	$0.377485\pi$
$678$	−18.8838	+	6.60773i	−0.725228	+	0.253768i
$679$	−0.447758	+	1.22391i	−0.0171834	+	0.0469695i
$680$	−8.45515	−	1.38943i	−0.324240	−	0.0532822i
$681$	−0.361855	−	4.82863i	−0.0138663	−	0.185033i
$682$	1.83822	+	3.47809i	0.0703892	+	0.133183i
$683$	40.2536	+	7.61639i	1.54026	+	0.291433i	0.885585	−	0.464478i	$-0.153758\pi$
$683$	40.2536	+	7.61639i	1.54026	+	0.291433i	0.654675	+	0.755911i	$0.272806\pi$
$684$	8.01189	+	1.20760i	0.306342	+	0.0461737i
$685$	6.93557	+	39.5201i	0.264994	+	1.50999i
$686$	−36.5321	+	14.1293i	−1.39480	+	0.539460i
$687$	−26.3219	+	26.3219i	−1.00424	+	1.00424i
$688$	0.423143	+	0.573339i	0.0161322	+	0.0218583i
$689$	−20.2583	+	13.8119i	−0.771779	+	0.526190i
$690$	5.28032	−	41.8620i	0.201018	−	1.59366i
$691$	5.76994	−	0.432397i	0.219499	−	0.0164492i	0.0354733	−	0.999371i	$-0.488706\pi$
$691$	5.76994	−	0.432397i	0.219499	−	0.0164492i	0.184026	+	0.982921i	$0.441087\pi$
$692$	31.4424	+	11.0022i	1.19526	+	0.418240i
$693$	0.532889	−	0.247420i	0.0202428	−	0.00939869i
$694$	−1.43120	+	2.97191i	−0.0543274	+	0.112812i
$695$	−4.22750	−	6.38097i	−0.160358	−	0.242044i
$696$	−0.502994	−	0.0376942i	−0.0190660	−	0.00142880i
$697$	−27.4589	−	11.9802i	−1.04008	−	0.453782i
$698$	−13.2331	+	25.0383i	−0.500882	+	0.947715i
$699$	−18.5132	+	23.2148i	−0.700234	+	0.878066i
$700$	19.3404	+	26.3852i	0.730997	+	0.997266i
$701$	4.17050	+	5.22964i	0.157518	+	0.197521i	0.854328	−	0.519735i	$-0.173969\pi$
$701$	4.17050	+	5.22964i	0.157518	+	0.197521i	−0.696810	+	0.717256i	$0.745398\pi$
$702$	−19.5127	+	3.69201i	−0.736461	+	0.139346i
$703$	−2.35353	+	0.0880629i	−0.0887651	+	0.00332136i
$704$	2.47189	+	1.42715i	0.0931629	+	0.0537876i
$705$	43.3192	+	3.82518i	1.63150	+	0.144065i
$706$	2.67784	+	0.611200i	0.100782	+	0.0230028i
$707$	1.37386	−	2.30385i	0.0516691	−	0.0866452i
$708$	32.1787	−	51.2121i	1.20935	−	1.92467i
$709$	19.4353	+	20.9462i	0.729906	+	0.786652i	0.983548	−	0.180646i	$-0.0578189\pi$
$709$	19.4353	+	20.9462i	0.729906	+	0.786652i	−0.253642	+	0.967298i	$0.581628\pi$
$710$	−15.6174	−	46.6075i	−0.586111	−	1.74915i
$711$	−0.347657	+	0.0524009i	−0.0130382	+	0.00196519i
$712$	−0.640516	−	0.0239664i	−0.0240044	−	0.000898180i
$713$	−28.0917	−	17.6512i	−1.05204	−	0.661041i
$714$	33.5884	+	25.5296i	1.25701	+	0.955421i
$715$	−1.27350	−	0.0645886i	−0.0476264	−	0.00241548i
$716$	−9.40014	−	16.2815i	−0.351300	−	0.608469i
$717$	30.4025	−	8.14633i	1.13540	−	0.304230i
$718$	1.69245	+	45.2318i	0.0631618	+	1.68804i
$719$	11.4410	+	7.80037i	0.426679	+	0.290905i	0.757557	−	0.652769i	$-0.226393\pi$
$719$	11.4410	+	7.80037i	0.426679	+	0.290905i	−0.330879	+	0.943673i	$0.607345\pi$
$720$	0.340010	+	5.51931i	0.0126714	+	0.205692i
$721$	−7.35033	+	25.9601i	−0.273741	+	0.966805i
$722$	−1.16947	−	10.3793i	−0.0435232	−	0.386279i
$723$	7.29546	+	3.85576i	0.271321	+	0.143397i
$724$	20.2953	+	51.7115i	0.754267	+	1.92184i
$725$	0.344957	+	1.23369i	0.0128114	+	0.0458180i
$726$	−42.3730	−	16.6302i	−1.57261	−	0.617203i
$727$	−3.23781	−	9.25314i	−0.120084	−	0.343180i	0.868114	−	0.496366i	$-0.165332\pi$
$727$	−3.23781	−	9.25314i	−0.120084	−	0.343180i	−0.988197	+	0.153186i	$0.951047\pi$
$728$	−4.58997	−	3.76760i	−0.170116	−	0.139637i
$729$	−6.60496	−	13.7153i	−0.244628	−	0.507976i
$730$	0.370237	−	0.622052i	0.0137031	−	0.0230232i
$731$	−0.284278	+	0.921606i	−0.0105144	+	0.0340868i
$732$	−8.86657	+	46.8610i	−0.327718	+	1.73203i
$733$	−26.4207	+	19.4993i	−0.975869	+	0.720224i	−0.960102	−	0.279651i	$-0.909781\pi$
$733$	−26.4207	+	19.4993i	−0.975869	+	0.720224i	−0.0157677	+	0.999876i	$0.505019\pi$
$734$	−35.0994			−1.29554
$735$	−4.46629	−	30.4814i	−0.164741	−	1.12432i
$736$	−36.2046			−1.33452
$737$	−2.33281	+	1.72169i	−0.0859300	+	0.0634192i
$738$	2.68668	−	14.1995i	0.0988982	−	0.522689i
$739$	−0.211761	+	0.686513i	−0.00778977	+	0.0252538i	−0.959384	−	0.282103i	$-0.908968\pi$
$739$	−0.211761	+	0.686513i	−0.00778977	+	0.0252538i	0.951594	+	0.307356i	$0.0994444\pi$
$740$	0.854291	+	3.36637i	0.0314043	+	0.123750i
$741$	7.18501	+	14.9198i	0.263948	+	0.548094i
$742$	0.863235	−	61.1399i	0.0316903	−	2.24451i
$743$	14.5426	+	41.5604i	0.533516	+	1.52470i	0.823298	+	0.567609i	$0.192132\pi$
$743$	14.5426	+	41.5604i	0.533516	+	1.52470i	−0.289782	+	0.957093i	$0.593583\pi$
$744$	−13.4129	−	5.26419i	−0.491743	−	0.192995i
$745$	−32.3228	+	39.4458i	−1.18421	+	1.44518i
$746$	17.4425	+	44.4427i	0.638614	+	1.62716i
$747$	12.7136	+	6.71933i	0.465166	+	0.245847i
$748$	0.269579	+	2.39258i	0.00985680	+	0.0874815i
$749$	−10.3878	+	11.7317i	−0.379563	+	0.428669i
$750$	−42.7009	+	18.5073i	−1.55922	+	0.675790i
$751$	−35.4686	−	24.1821i	−1.29427	−	0.882418i	−0.296900	−	0.954908i	$-0.595953\pi$
$751$	−35.4686	−	24.1821i	−1.29427	−	0.882418i	−0.997369	+	0.0724905i	$0.976905\pi$
$752$	−1.04575	−	27.9482i	−0.0381346	−	1.01917i
$753$	50.6222	−	13.5642i	1.84477	−	0.494306i
$754$	−0.607891	−	1.05290i	−0.0221381	−	0.0383443i
$755$	−13.5171	−	14.9614i	−0.491936	−	0.544501i
$756$	11.3027	−	24.9394i	0.411074	−	0.907035i
$757$	1.94910	+	1.22470i	0.0708411	+	0.0445124i	0.566987	−	0.823727i	$-0.308109\pi$
$757$	1.94910	+	1.22470i	0.0708411	+	0.0445124i	−0.496146	+	0.868239i	$0.665252\pi$
$758$	12.4117	+	0.464412i	0.450812	+	0.0168682i
$759$	−2.24225	+	0.337965i	−0.0813885	+	0.0122673i
$760$	7.95286	−	2.66487i	0.288480	−	0.0966652i
$761$	4.02980	+	4.34309i	0.146080	+	0.157437i	0.801853	−	0.597521i	$-0.203848\pi$
$761$	4.02980	+	4.34309i	0.146080	+	0.157437i	−0.655773	+	0.754958i	$0.727657\pi$
$762$	−45.0664	+	71.7228i	−1.63258	+	2.59824i
$763$	−18.8137	−	17.9574i	−0.681100	−	0.650102i
$764$	−39.6918	−	9.05940i	−1.43600	−	0.327758i
$765$	−5.73725	+	4.80624i	−0.207431	+	0.173770i
$766$	−47.8180	−	27.6077i	−1.72773	−	0.997508i
$767$	27.8624	−	1.04254i	1.00605	−	0.0376439i
$768$	11.6220	−	2.19900i	0.419372	−	0.0793494i
$769$	17.7573	+	22.2669i	0.640345	+	0.802967i	0.991046	−	0.133521i	$-0.0426282\pi$
$769$	17.7573	+	22.2669i	0.640345	+	0.802967i	−0.350701	+	0.936487i	$0.614057\pi$
$770$	1.95773	−	2.50595i	0.0705516	−	0.0903083i
$771$	−21.5875	+	27.0699i	−0.777456	+	0.974899i
$772$	10.2835	−	19.4574i	0.370112	−	0.700287i
$773$	6.65557	+	2.90379i	0.239384	+	0.104442i	0.516160	−	0.856492i	$-0.327361\pi$
$773$	6.65557	+	2.90379i	0.239384	+	0.104442i	−0.276776	+	0.960935i	$0.589266\pi$
$774$	−0.463932	−	0.0347669i	−0.0166757	−	0.00124967i
$775$	−0.971369	+	36.5808i	−0.0348926	+	1.31402i
$776$	0.213788	−	0.443935i	0.00767454	−	0.0159363i
$777$	0.772715	−	3.17799i	0.0277210	−	0.114010i
$778$	−60.6024	−	21.2057i	−2.17270	−	0.760261i
$779$	29.2434	−	2.19149i	1.04775	−	0.0785183i
$780$	19.2927	−	14.9708i	0.690790	−	0.536042i
$781$	−2.18264	+	1.48810i	−0.0781011	+	0.0532484i
$782$	−21.8093	−	29.5506i	−0.779901	−	1.05673i
$783$	0.758139	−	0.758139i	0.0270937	−	0.0270937i
$784$	−19.0896	+	5.30300i	−0.681772	+	0.189393i
$785$	−14.4602	+	2.53768i	−0.516106	+	0.0905738i
$786$	33.3762	+	5.03065i	1.19049	+	0.179437i
$787$	−11.9734	−	2.26548i	−0.426805	−	0.0807558i	−0.0319285	−	0.999490i	$-0.510165\pi$
$787$	−11.9734	−	2.26548i	−0.426805	−	0.0807558i	−0.394876	+	0.918734i	$0.629213\pi$
$788$	−11.3908	−	21.5524i	−0.405780	−	0.767773i
$789$	0.680052	+	9.07467i	0.0242105	+	0.323067i
$790$	−1.54599	+	1.10960i	−0.0550038	+	0.0394777i
$791$	12.0607	−	4.03002i	0.428829	−	0.143291i
$792$	−0.209666	+	0.0733655i	−0.00745017	+	0.00260693i
$793$	−20.1513	+	8.79192i	−0.715594	+	0.312210i
$794$	−2.03641	+	27.1740i	−0.0722695	+	0.964369i
$795$	46.7398	+	11.3228i	1.65769	+	0.401579i
$796$	−2.93436	−	9.51297i	−0.104006	−	0.337178i
$797$	−15.1671	+	1.70893i	−0.537248	+	0.0605333i	−0.376420	−	0.926449i	$-0.622845\pi$
$797$	−15.1671	+	1.70893i	−0.537248	+	0.0605333i	−0.160828	+	0.986982i	$0.551416\pi$
$798$	−40.7454	−	6.73099i	−1.44237	−	0.238275i
$799$	29.5952	−	23.6013i	1.04700	−	0.834956i
$800$	20.3407	+	34.3645i	0.719153	+	1.21497i
$801$	−0.380804	+	0.410409i	−0.0134550	+	0.0145011i
$802$	2.58287	+	9.63939i	0.0912042	+	0.340379i
$803$	−0.0375780	−	0.0100690i	−0.00132610	−	0.000355327i
$804$	12.3554	−	54.1326i	0.435742	−	1.90911i
$805$	−3.73149	+	26.5576i	−0.131518	+	0.936031i
$806$	−7.72825	−	33.8597i	−0.272216	−	1.19266i
$807$	1.80101	−	48.1330i	0.0633985	−	1.69436i
$808$	−0.602226	+	0.815988i	−0.0211863	+	0.0287064i
$809$	−4.54870	−	30.1787i	−0.159924	−	1.06103i	−0.914433	−	0.404736i	$-0.867363\pi$
$809$	−4.54870	−	30.1787i	−0.159924	−	1.06103i	0.754510	−	0.656289i	$-0.227875\pi$
$810$	40.9062	+	31.0373i	1.43730	+	1.09054i
$811$	23.0205	−	5.25427i	0.808358	−	0.184503i	0.201682	−	0.979451i	$-0.435359\pi$
$811$	23.0205	−	5.25427i	0.808358	−	0.184503i	0.606677	+	0.794949i	$0.292502\pi$
$812$	1.66967	+	0.148856i	0.0585939	+	0.00522382i
$813$	50.8431	−	31.9469i	1.78315	−	1.12043i
$814$	0.292373	−	0.168801i	0.0102477	−	0.00591649i
$815$	−9.15460	+	25.0890i	−0.320672	+	0.878830i
$816$	15.6434	+	14.5150i	0.547629	+	0.508125i
$817$	−0.175514	−	0.927611i	−0.00614044	−	0.0324530i
$818$	5.82377	+	0.656181i	0.203623	+	0.0229428i
$819$	−5.10956	+	0.892255i	−0.178542	+	0.0311779i
$820$	−12.1970	−	41.4892i	−0.425939	−	1.44887i
$821$	35.8825	−	11.0683i	1.25231	−	0.386286i	0.403496	−	0.914981i	$-0.367795\pi$
$821$	35.8825	−	11.0683i	1.25231	−	0.386286i	0.848811	+	0.528696i	$0.177319\pi$
$822$	−29.8693	+	68.4613i	−1.04181	+	2.38786i
$823$	−35.1068	+	30.2118i	−1.22375	+	1.05312i	−0.226886	+	0.973921i	$0.572855\pi$
$823$	−35.1068	+	30.2118i	−1.22375	+	1.05312i	−0.996859	+	0.0791969i	$0.974764\pi$
$824$	3.72678	−	9.49568i	0.129829	−	0.330798i
$825$	1.58054	+	1.93841i	0.0550275	+	0.0674867i
$826$	−37.8215	+	58.3475i	−1.31598	+	2.03017i
$827$	−1.07495	+	3.07204i	−0.0373798	+	0.106825i	−0.961061	−	0.276337i	$-0.910879\pi$
$827$	−1.07495	+	3.07204i	−0.0373798	+	0.106825i	0.923681	+	0.383162i	$0.125165\pi$
$828$	6.38908	−	7.42424i	0.222036	−	0.258010i
$829$	−40.7335	−	12.5646i	−1.41473	−	0.436387i	−0.509193	−	0.860652i	$-0.670056\pi$
$829$	−40.7335	−	12.5646i	−1.41473	−	0.436387i	−0.905538	+	0.424265i	$0.860532\pi$
$830$	77.8257	+	1.03311i	2.70137	+	0.0358599i
$831$	−4.64966	+	30.8485i	−0.161295	+	1.07012i
$832$	−17.8181	−	17.8181i	−0.617733	−	0.617733i
$833$	−21.1176	−	16.5265i	−0.731683	−	0.572608i
$834$		−	14.2490i		−	0.493402i
$835$	−55.8254	+	1.34710i	−1.93192	+	0.0466185i
$836$	−1.32765	−	1.94731i	−0.0459178	−	0.0673491i
$837$	27.0786	−	14.3115i	0.935975	−	0.494677i
$838$	12.8738	+	11.0788i	0.444717	+	0.382710i
$839$	−24.0017	+	11.5586i	−0.828632	+	0.399048i	−0.799602	−	0.600530i	$-0.794956\pi$
$839$	−24.0017	+	11.5586i	−0.828632	+	0.399048i	−0.0290301	+	0.999579i	$0.509242\pi$
$840$	0.551974	+	11.6344i	0.0190449	+	0.401424i
$841$	−26.0690	−	12.5541i	−0.898930	−	0.432902i
$842$	−28.7168	−	65.8196i	−0.989646	−	2.26829i
$843$	−3.07466	−	3.57282i	−0.105897	−	0.123054i
$844$	25.3578	−	9.95220i	0.872851	−	0.342569i
$845$	−16.9490	−	5.47549i	−0.583064	−	0.188363i
$846$	14.2761	+	11.3848i	0.490822	+	0.391418i
$847$	26.7805	+	10.9493i	0.920188	+	0.376224i
$848$	3.46292	−	30.7342i	0.118917	−	1.05542i
$849$	21.2012	−	31.0964i	0.727623	−	1.06723i
$850$	−15.7956	+	37.3032i	−0.541785	+	1.27949i
$851$	−1.42357	+	2.46570i	−0.0487995	+	0.0845232i
$852$	13.0936	−	48.8661i	0.448580	−	1.67412i
$853$	27.3951	+	43.5991i	0.937991	+	1.49280i	0.868778	+	0.495202i	$0.164906\pi$
$853$	27.3951	+	43.5991i	0.937991	+	1.49280i	0.0692125	+	0.997602i	$0.477951\pi$
$854$	10.9529	−	53.7241i	0.374802	−	1.83840i
$855$	2.76685	−	6.78364i	0.0946242	−	0.231996i
$856$	4.34290	−	4.02963i	0.148437	−	0.137730i
$857$	38.0585	+	28.0885i	1.30006	+	0.959484i	0.999985	+	0.00556723i	$0.00177211\pi$
$857$	38.0585	+	28.0885i	1.30006	+	0.959484i	0.300071	+	0.953917i	$0.402990\pi$
$858$	−1.90992	−	1.40959i	−0.0652036	−	0.0481225i
$859$	34.8050	−	32.2943i	1.18753	−	1.10187i	0.194883	−	0.980827i	$-0.437567\pi$
$859$	34.8050	−	32.2943i	1.18753	−	1.10187i	0.992648	−	0.121041i	$-0.0386232\pi$
$860$	−1.28330	+	0.539735i	−0.0437600	+	0.0184048i
$861$	−8.13511	+	39.9027i	−0.277244	+	1.35988i
$862$	34.0300	+	54.1584i	1.15907	+	1.84464i
$863$	−4.94295	+	18.4473i	−0.168260	+	0.627955i	0.829342	+	0.558742i	$0.188716\pi$
$863$	−4.94295	+	18.4473i	−0.168260	+	0.627955i	−0.997602	+	0.0692134i	$0.977951\pi$
$864$	16.7115	−	28.9452i	0.568538	−	0.984737i
$865$	16.3622	−	25.2889i	0.556333	−	0.859848i
$866$	22.5924	−	33.1370i	0.767723	−	1.12604i
$867$	0.512334	−	4.54709i	0.0173998	−	0.154427i
$868$	44.3239	+	18.1221i	1.50445	+	0.615104i
$869$	0.0799574	+	0.0637639i	0.00271237	+	0.00216304i
$870$	−0.733081	+	2.26920i	−0.0248538	+	0.0769332i
$871$	23.8270	−	9.35141i	0.807347	−	0.316860i
$872$	6.41403	+	7.45324i	0.217207	+	0.252399i
$873$	−0.172108	−	0.394476i	−0.00582497	−	0.0133510i
$874$	32.3907	+	15.5985i	1.09563	+	0.527628i
$875$	27.3042	−	11.3789i	0.923051	−	0.384678i
$876$	0.671253	−	0.323259i	0.0226796	−	0.0109219i
$877$	39.2481	+	33.7758i	1.32532	+	1.14053i	0.979326	+	0.202288i	$0.0648377\pi$
$877$	39.2481	+	33.7758i	1.32532	+	1.14053i	0.345989	+	0.938238i	$0.387543\pi$
$878$	7.86695	−	4.15781i	0.265497	−	0.140319i
$879$	−27.7890	−	40.7590i	−0.937300	−	1.37477i
$880$	1.10962	−	1.16449i	0.0374052	−	0.0392551i
$881$		−	12.1128i		−	0.408091i	−0.978961	−	0.204046i	$-0.934591\pi$
$881$		−	12.1128i		−	0.408091i	0.978961	−	0.204046i	$-0.0654091\pi$
$882$	5.50539	−	11.7053i	0.185376	−	0.394136i
$883$	−37.0414	−	37.0414i	−1.24654	−	1.24654i	−0.957236	−	0.289308i	$-0.906575\pi$
$883$	−37.0414	−	37.0414i	−1.24654	−	1.24654i	−0.289308	−	0.957236i	$-0.593425\pi$
$884$	3.16807	−	21.0188i	0.106554	−	0.706938i
$885$	−38.1540	−	39.1806i	−1.28253	−	1.31704i
$886$	76.0233	+	23.4501i	2.55405	+	0.787821i
$887$	3.37647	−	3.92353i	0.113371	−	0.131739i	−0.698419	−	0.715689i	$-0.746113\pi$
$887$	3.37647	−	3.92353i	0.113371	−	0.131739i	0.811790	+	0.583950i	$0.198494\pi$
$888$	−0.408403	+	1.16715i	−0.0137051	+	0.0391670i
$889$	29.2851	−	45.1783i	0.982190	−	1.51523i
$890$	−0.823080	+	2.91637i	−0.0275897	+	0.0977569i
$891$	1.00818	−	2.56880i	0.0337752	−	0.0860579i
$892$	−3.50401	+	3.01545i	−0.117323	+	0.100965i
$893$	−14.8174	+	33.9619i	−0.495846	+	1.13649i
$894$	−90.7172	+	27.9826i	−3.03404	+	0.935877i
$895$	−16.3091	+	4.79456i	−0.545154	+	0.160265i
$896$	20.2736	−	3.54028i	0.677295	−	0.118272i
$897$	19.8930	+	2.24141i	0.664209	+	0.0748384i
$898$	0.991555	+	5.24050i	0.0330886	+	0.174878i
$899$	1.37452	+	1.27537i	0.0458430	+	0.0425360i
$900$	−10.6365	−	1.89321i	−0.354549	−	0.0631069i
$901$	36.2528	−	20.9306i	1.20776	−	0.697298i
$902$	−3.55933	+	2.23648i	−0.118513	+	0.0744665i
$903$	1.30583	+	0.116418i	0.0434552	+	0.00387416i
$904$	−4.68719	+	1.06982i	−0.155894	+	0.0355817i
$905$	49.7638	−	6.82643i	1.65421	−	0.226918i
$906$	−5.59431	−	37.1158i	−0.185859	−	1.23309i
$907$	2.22737	−	3.01798i	0.0739585	−	0.100210i	−0.766057	−	0.642773i	$-0.777784\pi$
$907$	2.22737	−	3.01798i	0.0739585	−	0.100210i	0.840015	+	0.542563i	$0.182546\pi$
$908$	0.227490	−	6.07981i	0.00754953	−	0.201765i
$909$	0.197117	+	0.863626i	0.00653796	+	0.0286447i
$910$	−22.4205	+	16.8963i	−0.743232	+	0.560106i
$911$	4.01101	−	17.5734i	0.132891	−	0.582232i	−0.864004	−	0.503485i	$-0.832051\pi$
$911$	4.01101	−	17.5734i	0.132891	−	0.582232i	0.996895	−	0.0787469i	$-0.0250919\pi$
$912$	−20.1773	−	5.40649i	−0.668137	−	0.179027i
$913$	−1.08261	−	4.04035i	−0.0358292	−	0.133716i
$914$	27.6553	−	29.8053i	0.914756	−	0.985872i
$915$	39.2931	+	17.7679i	1.29899	+	0.587389i
$916$	−36.5678	+	29.1619i	−1.20823	+	0.963535i
$917$	−21.1667	−	3.49667i	−0.698987	−	0.115470i
$918$	33.6923	−	3.79621i	1.11201	−	0.125294i
$919$	−10.7506	−	34.8526i	−0.354629	−	1.14968i	−0.940648	−	0.339383i	$-0.889782\pi$
$919$	−10.7506	−	34.8526i	−0.354629	−	1.14968i	0.586019	−	0.810297i	$-0.300694\pi$
$920$	2.38727	−	9.85447i	0.0787058	−	0.324892i
$921$	−0.891581	+	11.8973i	−0.0293786	+	0.392030i
$922$	−51.8909	+	22.6398i	−1.70894	+	0.745601i
$923$	22.0127	−	7.70259i	0.724558	−	0.253534i
$924$	3.10417	−	1.03724i	0.102120	−	0.0341228i
$925$	3.14018	−	0.0340789i	0.103249	−	0.00112051i
$926$	4.82740	+	64.4172i	0.158638	+	2.11688i
$927$	−4.16342	−	7.87758i	−0.136745	−	0.258734i
$928$	2.01052	+	0.380411i	0.0659985	+	0.0124876i
$929$	27.4640	+	4.13953i	0.901064	+	0.135814i	0.583206	−	0.812325i	$-0.301798\pi$
$929$	27.4640	+	4.13953i	0.901064	+	0.135814i	0.317859	+	0.948138i	$0.397036\pi$
$930$	−39.1179	+	55.7703i	−1.28273	+	1.82878i
$931$	25.8349	+	4.64343i	0.846705	+	0.152182i
$932$	−26.3810	+	26.3810i	−0.864139	+	0.864139i
$933$	1.74237	+	2.36083i	0.0570427	+	0.0772901i
$934$	−74.6801	+	50.9160i	−2.44361	+	1.66602i
$935$	2.15996	+	0.272449i	0.0706381	+	0.00891003i
$936$	1.95557	−	0.146550i	0.0639198	−	0.00479013i
$937$	17.8861	+	6.25863i	0.584315	+	0.204461i	0.606217	−	0.795299i	$-0.292686\pi$
$937$	17.8861	+	6.25863i	0.584315	+	0.204461i	−0.0219018	+	0.999760i	$0.506972\pi$
$938$	−15.0815	+	62.0264i	−0.492428	+	2.02524i
$939$	6.74841	−	14.0132i	0.220226	−	0.457304i
$940$	53.5492	+	10.8702i	1.74658	+	0.354547i
$941$	2.15796	+	0.161716i	0.0703473	+	0.00527180i	0.109857	−	0.993947i	$-0.464961\pi$
$941$	2.15796	+	0.161716i	0.0703473	+	0.00527180i	−0.0395099	+	0.999219i	$0.512580\pi$
$942$	−25.0496	−	10.9290i	−0.816159	−	0.356087i
$943$	16.5652	−	31.3429i	0.539438	−	1.02067i
$944$	−21.9289	+	27.4980i	−0.713726	+	0.894984i
$945$	−19.5101	−	15.2419i	−0.634664	−	0.495819i
$946$	0.0843754	+	0.105803i	0.00274328	+	0.00343996i
$947$	−39.6854	+	7.50889i	−1.28960	+	0.244006i	−0.785081	−	0.619393i	$-0.787379\pi$
$947$	−39.6854	+	7.50889i	−1.28960	+	0.244006i	−0.504522	+	0.863399i	$0.668331\pi$
$948$	−1.95717	+	0.0732321i	−0.0635659	+	0.00237847i
$949$	0.297440	+	0.171727i	0.00965531	+	0.00557450i
$950$	−3.39224	−	39.5081i	−0.110059	−	1.28181i
$951$	−28.7475	−	6.56143i	−0.932202	−	0.212769i
$952$	7.33392	+	7.00013i	0.237694	+	0.226876i
$953$	4.88815	−	7.77944i	0.158343	−	0.252001i	−0.758125	−	0.652109i	$-0.773885\pi$
$953$	4.88815	−	7.77944i	0.158343	−	0.252001i	0.916468	+	0.400108i	$0.131027\pi$
$954$	13.7347	+	14.8025i	0.444677	+	0.479248i
$955$	−16.4112	+	32.9519i	−0.531053	+	1.06630i
$956$	39.1058	−	5.89426i	1.26477	−	0.190634i
$957$	0.128068	+	0.00479196i	0.00413985	+	0.000154902i
$958$	38.9536	+	24.4762i	1.25853	+	0.790790i
$959$	19.5975	−	43.2418i	0.632835	−	1.39635i
$960$	−2.50351	+	49.3621i	−0.0808004	+	1.59315i
$961$	11.2819	+	19.5409i	0.363934	+	0.630351i
$962$	−2.87891	+	0.771402i	−0.0928199	+	0.0248710i
$963$	−0.193492	−	5.17119i	−0.00623520	−	0.166639i
$964$	8.56649	+	5.84054i	0.275908	+	0.188111i
$965$	−14.9096	−	13.1792i	−0.479957	−	0.424255i
$966$	−33.0959	+	37.3777i	−1.06484	+	1.20261i
$967$	5.18225	+	45.9937i	0.166650	+	1.47906i	0.747072	+	0.664743i	$0.231459\pi$
$967$	5.18225	+	45.9937i	0.166650	+	1.47906i	−0.580422	+	0.814316i	$0.697112\pi$
$968$	−9.67111	−	5.11133i	−0.310841	−	0.164284i
$969$	−10.3292	−	26.3184i	−0.331822	−	0.845468i
$970$	−1.80183	−	1.47646i	−0.0578532	−	0.0474062i
$971$	−15.0692	−	5.91421i	−0.483593	−	0.189796i	0.111005	−	0.993820i	$-0.464593\pi$
$971$	−15.0692	−	5.91421i	−0.483593	−	0.189796i	−0.594597	+	0.804024i	$0.702688\pi$
$972$	7.20024	+	20.5771i	0.230948	+	0.660011i
$973$	−0.127859	+	9.05580i	−0.00409897	+	0.290316i
$974$	−13.0924	−	27.1867i	−0.419508	−	0.871118i
$975$	−9.04896	−	20.1412i	−0.289799	−	0.645036i
$976$	8.17462	−	26.5015i	0.261663	−	0.848292i
$977$	−3.47561	+	18.3690i	−0.111195	+	0.587677i	0.882004	+	0.471242i	$0.156194\pi$
$977$	−3.47561	+	18.3690i	−0.111195	+	0.587677i	−0.993198	+	0.116435i	$0.962853\pi$
$978$	−40.0021	+	29.5229i	−1.27913	+	0.944037i
$979$	0.162854			0.00520484
$980$	−1.28835	−	38.6867i	−0.0411547	−	1.23580i
$981$	8.58896			0.274224
$982$	−24.7901	+	18.2960i	−0.791085	+	0.583847i
$983$	3.32845	−	17.5913i	0.106161	−	0.561075i	−0.888586	−	0.458710i	$-0.848312\pi$
$983$	3.32845	−	17.5913i	0.106161	−	0.561075i	0.994747	−	0.102365i	$-0.0326408\pi$
$984$	4.53827	−	14.7127i	0.144675	−	0.469024i
$985$	−21.3649	+	5.42180i	−0.680742	+	0.172753i
$986$	0.900624	+	1.87016i	0.0286817	+	0.0595582i
$987$	−39.7726	−	32.6467i	−1.26597	−	1.03916i
$988$	6.87209	+	19.6393i	0.218630	+	0.624810i
$989$	−1.06238	−	0.416955i	−0.0337818	−	0.0132584i
$990$	0.103720	+	1.04504i	0.00329644	+	0.0332135i
$991$	−14.6638	−	37.3628i	−0.465812	−	1.18687i	−0.950096	−	0.311958i	$-0.899015\pi$
$991$	−14.6638	−	37.3628i	−0.465812	−	1.18687i	0.484284	−	0.874911i	$-0.339080\pi$
$992$	51.6784	+	27.3128i	1.64079	+	0.867184i
$993$	3.34117	+	29.6537i	0.106029	+	0.941031i
$994$	−15.8446	+	55.9604i	−0.502560	+	1.77496i
$995$	−8.98454	+	0.553480i	−0.284829	+	0.0175465i
$996$	66.1863	+	45.1251i	2.09719	+	1.42984i
$997$	0.348565	+	9.31559i	0.0110392	+	0.295028i	0.993873	+	0.110532i	$0.0352556\pi$
$997$	0.348565	+	9.31559i	0.0110392	+	0.295028i	−0.982833	+	0.184495i	$0.940935\pi$
$998$	5.02100	−	1.34537i	0.158937	−	0.0425870i
$999$	−1.31420	−	2.27627i	−0.0415796	−	0.0720179i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.x.a.108.23	yes	624
5.2	odd	4	inner	245.2.x.a.157.23	yes	624
49.5	odd	42	inner	245.2.x.a.103.23	✓	624
245.152	even	84	inner	245.2.x.a.152.23	yes	624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.x.a.103.23	✓	624	49.5	odd	42	inner
245.2.x.a.108.23	yes	624	1.1	even	1	trivial
245.2.x.a.152.23	yes	624	245.152	even	84	inner
245.2.x.a.157.23	yes	624	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70168 - 1.25589i) q^{2} +(0.365908 - 1.93387i) q^{3} +(0.728921 - 2.36310i) q^{4} +(-1.92148 - 1.14364i) q^{5} +(-1.80608 - 3.75036i) q^{6} +(1.11418 + 2.39971i) q^{7} +(-0.330380 - 0.944171i) q^{8} +(-0.813339 - 0.319212i) q^{9} +(-4.70603 + 0.467072i) q^{10} +(0.0928530 + 0.236585i) q^{11} +(-4.30321 - 2.27432i) q^{12} +(-0.251221 - 2.22965i) q^{13} +(4.90975 + 2.68423i) q^{14} +(-2.91473 + 3.29743i) q^{15} +(2.33855 + 1.59440i) q^{16} +(0.143238 + 3.82813i) q^{17} +(-1.78494 + 0.478272i) q^{18} +(-1.87492 - 3.24746i) q^{19} +(-4.10315 + 3.70704i) q^{20} +(5.04841 - 1.27661i) q^{21} +(0.455132 + 0.285978i) q^{22} +(-4.52997 - 0.169500i) q^{23} +(-1.94679 + 0.293432i) q^{24} +(2.38418 + 4.39496i) q^{25} +(-3.22770 - 3.47863i) q^{26} +(2.22649 - 3.54343i) q^{27} +(6.48291 - 0.883728i) q^{28} +(0.249778 + 0.0570102i) q^{29} +(-0.818715 + 9.27175i) q^{30} +(6.33821 + 3.65937i) q^{31} +(7.98106 - 0.298630i) q^{32} +(0.491501 - 0.0929970i) q^{33} +(5.05147 + 6.33434i) q^{34} +(0.603523 - 5.88522i) q^{35} +(-1.34719 + 1.68932i) q^{36} +(0.293479 - 0.555290i) q^{37} +(-7.26897 - 3.17142i) q^{38} +(-4.40377 - 0.330017i) q^{39} +(-0.444973 + 2.19204i) q^{40} +(-3.39316 + 7.04597i) q^{41} +(6.98747 - 8.51264i) q^{42} +(0.237634 + 0.0831519i) q^{43} +(0.626758 - 0.0469691i) q^{44} +(1.19775 + 1.54353i) q^{45} +(-7.92142 + 5.40073i) q^{46} +(-5.86776 - 7.95053i) q^{47} +(3.93905 - 3.93905i) q^{48} +(-4.51720 + 5.34742i) q^{49} +(9.57670 + 4.48453i) q^{50} +(7.45551 + 1.12374i) q^{51} +(-5.45201 - 1.03158i) q^{52} +(-5.10608 - 9.66117i) q^{53} +(-0.661417 - 8.82600i) q^{54} +(0.0921533 - 0.560785i) q^{55} +(1.89763 - 1.84479i) q^{56} +(-6.96621 + 2.43758i) q^{57} +(0.496640 - 0.216682i) q^{58} +(-0.928629 + 12.3917i) q^{59} +(5.66755 + 9.29138i) q^{60} +(-2.88820 - 9.36330i) q^{61} +(15.3814 - 1.73306i) q^{62} +(-0.140191 - 2.30744i) q^{63} +(8.78041 - 7.00214i) q^{64} +(-2.06720 + 4.57154i) q^{65} +(0.719581 - 0.775524i) q^{66} +(2.95256 + 11.0191i) q^{67} +(9.15067 + 2.45192i) q^{68} +(-1.98534 + 8.69835i) q^{69} +(-6.36421 - 10.7727i) q^{70} +(2.31287 + 10.1333i) q^{71} +(-0.0326800 + 0.873392i) q^{72} +(-0.0908966 + 0.123161i) q^{73} +(-0.197979 - 1.31350i) q^{74} +(9.37167 - 3.00253i) q^{75} +(-9.04075 + 2.06349i) q^{76} +(-0.464281 + 0.486419i) q^{77} +(-7.90826 + 4.96909i) q^{78} +(0.348481 - 0.201196i) q^{79} +(-2.67006 - 5.73806i) q^{80} +(-7.95933 - 7.38518i) q^{81} +(3.07493 + 16.2514i) q^{82} +(-16.3546 - 1.84272i) q^{83} +(0.663132 - 12.8605i) q^{84} +(4.10277 - 7.51949i) q^{85} +(0.508807 - 0.156946i) q^{86} +(0.201646 - 0.462178i) q^{87} +(0.192700 - 0.165832i) q^{88} +(0.234099 - 0.596475i) q^{89} +(3.97669 + 1.12233i) q^{90} +(5.07060 - 3.08709i) q^{91} +(-3.70254 + 10.5812i) q^{92} +(9.39594 - 10.9183i) q^{93} +(-19.9700 - 6.15994i) q^{94} +(-0.111297 + 8.38416i) q^{95} +(2.34282 - 15.5436i) q^{96} +(0.348307 + 0.348307i) q^{97} +(-0.971017 + 14.7727i) q^{98} -0.222064i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} - 34 q^{10} - 56 q^{11} - 34 q^{12} - 28 q^{13} + 12 q^{15} - 100 q^{16} - 26 q^{17} - 10 q^{18} - 28 q^{20} - 76 q^{21} - 48 q^{22}+ \cdots + 304 q^{98}+O(q^{100}) \) 624 * q - 26 * q^2 - 22 * q^3 - 28 * q^5 - 28 * q^6 - 18 * q^7 - 24 * q^8 - 34 * q^10 - 56 * q^11 - 34 * q^12 - 28 * q^13 + 12 * q^15 - 100 * q^16 - 26 * q^17 - 10 * q^18 - 28 * q^20 - 76 * q^21 - 48 * q^22 - 34 * q^23 - 24 * q^25 - 60 * q^26 - 28 * q^27 - 46 * q^28 - 10 * q^30 - 60 * q^31 + 54 * q^32 - 28 * q^33 - 20 * q^35 + 116 * q^36 - 20 * q^37 + 12 * q^38 - 46 * q^40 - 114 * q^42 - 24 * q^43 + 60 * q^45 + 108 * q^46 - 94 * q^47 - 296 * q^50 + 52 * q^51 - 52 * q^52 - 106 * q^53 + 14 * q^55 + 96 * q^56 + 72 * q^57 - 142 * q^58 - 26 * q^60 + 80 * q^61 - 56 * q^62 - 24 * q^63 - 20 * q^65 - 240 * q^66 - 8 * q^67 - 30 * q^68 + 180 * q^70 + 48 * q^71 + 138 * q^72 - 4 * q^73 - 106 * q^75 + 56 * q^76 - 8 * q^77 - 204 * q^78 - 18 * q^80 - 284 * q^81 - 162 * q^82 + 182 * q^83 - 36 * q^85 - 76 * q^86 - 74 * q^87 + 288 * q^88 - 112 * q^90 + 44 * q^91 - 8 * q^92 + 368 * q^93 + 26 * q^95 + 136 * q^96 + 304 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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